Runge-Kutta 10 und 12 eingefuegt, Algorithmus fuer RK14 ist da, aber noch nicht implementiert

8 files changed, 2168 insertions, 217 deletions

diff --git a/Physikunit.pas b/Physikunit.pas
index da9d56e..6f9f60c 100644
--- a/Physikunit.pas
+++ b/Physikunit.pas
@@ -15,7 +15,7 @@ uses
   Classes, SysUtils, Math, protokollunit, matheunit, mystringlistunit, lowlevelunit, baseUnix;
 
 type
-  tZeitverfahren = (zfEulerVorwaerts,zfRungeKuttaDreiAchtel,zfRungeKuttaVier);
+  tZeitverfahren = (zfEulerVorwaerts,zfRungeKuttaDreiAchtel,zfRungeKuttaVier,zfRungeKuttaZehn,zfRungeKuttaZwoelf,zfRungeKuttaVierzehn);
   tVerteilungsfunktion = function(x: extended): extended;
   tEMFeldInhalt = (
     efA,efAX,efAY,efAZ,
@@ -87,6 +87,18 @@ type
     procedure liKo(in1,in2,in3: tWertePunkt; fak2,fak3: extended); overload;
     procedure liKo(in1,in2,in3,in4: tWertePunkt; fak2,fak3,fak4: extended); overload;
     procedure liKo(in1,in2,in3,in4,in5: tWertePunkt; fak2,fak3,fak4,fak5: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6: tWertePunkt; fak2,fak3,fak4,fak5,fak6: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23: tWertePunkt; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23: extended); overload;
     function maxDT: extended;
   end;
 
@@ -109,6 +121,18 @@ type
     procedure liKo(in1,in2,in3: tFelder; fak2,fak3: extended); overload;
     procedure liKo(in1,in2,in3,in4: tFelder; fak2,fak3,fak4: extended); overload;
     procedure liKo(in1,in2,in3,in4,in5: tFelder; fak2,fak3,fak4,fak5: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6: tFelder; fak2,fak3,fak4,fak5,fak6: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7: tFelder; fak2,fak3,fak4,fak5,fak6,fak7: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22: extended); overload;
+    procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23: extended); overload;
     function maxDT: extended;
   end;
 
@@ -572,126 +596,6 @@ begin
   emWerte[efAZ,true]:=emWerte[efDAZDT,false];// + emWerte[efDAZDT,true]*dT;
 end;
 
-procedure tWertePunkt.liKo(in1,in2: tWertePunkt; fak2: extended); // Werte werden auf (in1 + fak2*in2') gesetzt
-var
-  emF: tEMFeldInhalt;
-  maF: tMaterieFeldInhalt;
-  i:   longint;
-begin
-(*  tEMFeldInhalt = (
-      efA,efAX,efAY,efAZ,
-      efDAXDT,efDAYDT,efDAZDT,
-      efDPhiDX
-    ); *)
-  for emF:=efAX to efDPhiDX do // alles außer efA, welchen Ableitung ja nicht berechnet wurde
-    emWerte[emF,false]:= in1.emWerte[emF,false] + fak2 * in2.emWerte[emF,true];
-
-(*  tMaterieFeldInhalt = (
-      mfN,mfDPsiDX,
-      mfP,mfPX,mfPY,mfPZ,
-      mfGamma,mfIGamma
-    ); *)
-  for i:=0 to length(matWerte)-1 do // siehe oben
-    for maF:=mfN to mfDPsiDX do
-      matWerte[i,maF,false]:= in1.matWerte[i,maF,false] + fak2 * in2.matWerte[i,maF,true];
-end;
-
-procedure tWertePunkt.liKo(in1,in2,in3: tWertePunkt; fak2,fak3: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  emF: tEMFeldInhalt;
-  maF: tMaterieFeldInhalt;
-  i:   longint;
-begin
-(*  tEMFeldInhalt = (
-      efA,efAX,efAY,efAZ,
-      efDAXDT,efDAYDT,efDAZDT,
-      efDPhiDX
-    ); *)
-  for emF:=efAX to efDPhiDX do // alles außer efA, welchen Ableitung ja nicht berechnet wurde
-    emWerte[emF,false]:=
-      in1.emWerte[emF,false]
-      + fak2 * in2.emWerte[emF,true]
-      + fak3 * in3.emWerte[emF,true];
-
-(*  tMaterieFeldInhalt = (
-      mfN,mfDPsiDX,
-      mfP,mfPX,mfPY,mfPZ,
-      mfGamma,mfIGamma
-    ); *)
-  for i:=0 to length(matWerte)-1 do // siehe oben
-    for maF:=mfN to mfDPsiDX do
-      matWerte[i,maF,false]:=
-        in1.matWerte[i,maF,false]
-        + fak2 * in2.matWerte[i,maF,true]
-        + fak3 * in3.matWerte[i,maF,true];
-end;
-
-procedure tWertePunkt.liKo(in1,in2,in3,in4: tWertePunkt; fak2,fak3,fak4: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  emF: tEMFeldInhalt;
-  maF: tMaterieFeldInhalt;
-  i:   longint;
-begin
-(*  tEMFeldInhalt = (
-      efA,efAX,efAY,efAZ,
-      efDAXDT,efDAYDT,efDAZDT,
-      efDPhiDX
-    ); *)
-  for emF:=efAX to efDPhiDX do // alles außer efA, welchen Ableitung ja nicht berechnet wurde
-    emWerte[emF,false]:=
-      in1.emWerte[emF,false]
-      + fak2 * in2.emWerte[emF,true]
-      + fak3 * in3.emWerte[emF,true]
-      + fak4 * in4.emWerte[emF,true];
-
-(*  tMaterieFeldInhalt = (
-      mfN,mfDPsiDX,
-      mfP,mfPX,mfPY,mfPZ,
-      mfGamma,mfIGamma
-    ); *)
-  for i:=0 to length(matWerte)-1 do // siehe oben
-    for maF:=mfN to mfDPsiDX do
-      matWerte[i,maF,false]:=
-        in1.matWerte[i,maF,false]
-        + fak2 * in2.matWerte[i,maF,true]
-        + fak3 * in3.matWerte[i,maF,true]
-        + fak4 * in4.matWerte[i,maF,true];
-end;
-
-procedure tWertePunkt.liKo(in1,in2,in3,in4,in5: tWertePunkt; fak2,fak3,fak4,fak5: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  emF: tEMFeldInhalt;
-  maF: tMaterieFeldInhalt;
-  i:   longint;
-begin
-(*  tEMFeldInhalt = (
-      efA,efAX,efAY,efAZ,
-      efDAXDT,efDAYDT,efDAZDT,
-      efDPhiDX
-    ); *)
-  for emF:=efAX to efDPhiDX do // alles außer efA, welchen Ableitung ja nicht berechnet wurde
-    emWerte[emF,false]:=
-      in1.emWerte[emF,false]
-      + fak2 * in2.emWerte[emF,true]
-      + fak3 * in3.emWerte[emF,true]
-      + fak4 * in4.emWerte[emF,true]
-      + fak5 * in5.emWerte[emF,true];
-
-(*  tMaterieFeldInhalt = (
-      mfN,mfDPsiDX,
-      mfP,mfPX,mfPY,mfPZ,
-      mfGamma,mfIGamma
-    ); *)
-  for i:=0 to length(matWerte)-1 do // siehe oben
-    for maF:=mfN to mfDPsiDX do
-      matWerte[i,maF,false]:=
-        in1.matWerte[i,maF,false]
-        + fak2 * in2.matWerte[i,maF,true]
-        + fak3 * in3.matWerte[i,maF,true]
-        + fak4 * in4.matWerte[i,maF,true]
-        + fak5 * in5.matWerte[i,maF,true];
-end;
-
 function tWertePunkt.maxDT: extended;
 var
   i: longint;
@@ -703,6 +607,41 @@ begin
       result:=min(result,-matWerte[i,mfN,false]/matWerte[i,mfN,true]);
 end;
 
+
+{ linearkombinationsspezifische Methoden von tWertePunkt und tFelder }
+
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA3}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA4}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA5}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA6}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA7}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA8}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA9}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA10}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA11}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA12}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA14}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA15}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA16}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA22}
+{$INCLUDE linearkombination.inc}
+{$DEFINE lkA23}
+{$INCLUDE linearkombination.inc}
+
 { tFelder }
 
 constructor tFelder.create(groesse: longint; teilchen: array of tTeilchenSpezies; lichter: tMyStringList; parent: tGitter);
@@ -802,38 +741,6 @@ begin
     inhalt[i].berechneAbleitungen(dX,iDX);
 end;
 
-procedure tFelder.liKo(in1,in2: tFelder; fak2: extended); // Werte werden auf (in1 + fak2*in2') gesetzt
-var
-  i: longint;
-begin
-  for i:=0 to length(inhalt)-1 do
-    inhalt[i].liKo(in1.inhalt[i],in2.inhalt[i],fak2);
-end;
-
-procedure tFelder.liKo(in1,in2,in3: tFelder; fak2,fak3: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  i: longint;
-begin
-  for i:=0 to length(inhalt)-1 do
-    inhalt[i].liKo(in1.inhalt[i],in2.inhalt[i],in3.inhalt[i],fak2,fak3);
-end;
-
-procedure tFelder.liKo(in1,in2,in3,in4: tFelder; fak2,fak3,fak4: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  i: longint;
-begin
-  for i:=0 to length(inhalt)-1 do
-    inhalt[i].liKo(in1.inhalt[i],in2.inhalt[i],in3.inhalt[i],in4.inhalt[i],fak2,fak3,fak4);
-end;
-
-procedure tFelder.liKo(in1,in2,in3,in4,in5: tFelder; fak2,fak3,fak4,fak5: extended); // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-var
-  i: longint;
-begin
-  for i:=0 to length(inhalt)-1 do
-    inhalt[i].liKo(in1.inhalt[i],in2.inhalt[i],in3.inhalt[i],in4.inhalt[i],in5.inhalt[i],fak2,fak3,fak4,fak5);
-end;
-
 function tFelder.maxDT: extended;
 var
   i: longint;
@@ -866,6 +773,12 @@ begin
       Setlength(Felders,2);
     zfRungeKuttaDreiAchtel,zfRungeKuttaVier:
       Setlength(Felders,5);
+    zfRungeKuttaZehn:
+      Setlength(Felders,18);
+    zfRungeKuttaZwoelf:
+      Setlength(Felders,26);
+    zfRungeKuttaVierzehn:
+      Setlength(Felders,36);
   end{of Case};
   xl:=dX/2;
 
@@ -1026,6 +939,592 @@ begin
             dT/6
           ); // y(t+dt) = y(t) + (y' + 2(ya' + yb') + yc') dt/6
         end;
+      zfRungeKuttaZehn: begin                // Quelle:  http://sce.uhcl.edu/rungekutta/rk108.txt
+        felders[2].liKo(felders[aktuelleFelder],felders[aktuelleFelder],dT*0.1);
+        felders[2].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(2,mDT,dT) then
+          continue;
+
+        felders[3].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],
+          -0.915176561375291440520015019275342154318951387664369720564660 * dT,
+           1.45453440217827322805250021715664459117622483736537873607016  * dT);
+        felders[3].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(3,mDT,dT) then
+          continue;
+
+        felders[4].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],
+          0.202259190301118170324681949205488413821477543637878380814562 * dT,
+          0.606777570903354510974045847616465241464432630913635142443687 * dT);
+        felders[4].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(4,mDT,dT) then
+          continue;
+
+        felders[5].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[4],
+          0.184024714708643575149100693471120664216774047979591417844635 * dT,
+          0.197966831227192369068141770510388793370637287463360401555746 * dT,
+         -0.0729547847313632629185146671595558023015011608914382961421311* dT);
+        felders[5].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(5,mDT,dT) then
+          continue;
+
+        felders[6].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],
+          0.0879007340206681337319777094132125475918886824944548534041378* dT,
+          0.410459702520260645318174895920453426088035325902848695210406 * dT,
+          0.482713753678866489204726942976896106809132737721421333413261 * dT);
+        felders[6].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(6,mDT,dT) then
+          continue;
+
+        felders[7].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],felders[6],
+          0.0859700504902460302188480225945808401411132615636600222593880* dT,
+          0.330885963040722183948884057658753173648240154838402033448632 * dT,
+          0.489662957309450192844507011135898201178015478433790097210790 * dT,
+         -0.0731856375070850736789057580558988816340355615025188195854775* dT);
+        felders[7].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(7,mDT,dT) then
+          continue;
+
+        felders[8].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[5],felders[6],felders[7],
+          0.120930449125333720660378854927668953958938996999703678812621 * dT,
+          0.260124675758295622809007617838335174368108756484693361887839 * dT,
+          0.0325402621549091330158899334391231259332716675992700000776101* dT,
+         -0.0595780211817361001560122202563305121444953672762930724538856* dT);
+        felders[8].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(8,mDT,dT) then
+          continue;
+
+        felders[9].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],
+          0.110854379580391483508936171010218441909425780168656559807038 * dT,
+         -0.0605761488255005587620924953655516875526344415354339234619466* dT,
+          0.321763705601778390100898799049878904081404368603077129251110 * dT,
+          0.510485725608063031577759012285123416744672137031752354067590 * dT);
+        felders[9].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(9,mDT,dT) then
+          continue;
+
+        felders[10].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],
+          0.112054414752879004829715002761802363003717611158172229329393 * dT,
+         -0.144942775902865915672349828340980777181668499748506838876185 * dT,
+         -0.333269719096256706589705211415746871709467423992115497968724 * dT,
+          0.499269229556880061353316843969978567860276816592673201240332 * dT,
+          0.509504608929686104236098690045386253986643232352989602185060 * dT);
+        felders[10].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(10,mDT,dT) then
+          continue;
+
+        felders[11].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],felders[10],
+          0.113976783964185986138004186736901163890724752541486831640341 * dT,
+         -0.0768813364203356938586214289120895270821349023390922987406384* dT,
+          0.239527360324390649107711455271882373019741311201004119339563 * dT,
+          0.397774662368094639047830462488952104564716416343454639902613 * dT,
+          0.0107558956873607455550609147441477450257136782823280838547024* dT,
+         -0.327769124164018874147061087350233395378262992392394071906457 * dT);
+        felders[11].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(11,mDT,dT) then
+          continue;
+
+        felders[12].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],felders[10],felders[11],
+          0.0798314528280196046351426864486400322758737630423413945356284* dT,
+         -0.0520329686800603076514949887612959068721311443881683526937298* dT,
+         -0.0576954146168548881732784355283433509066159287152968723021864* dT,
+          0.194781915712104164976306262147382871156142921354409364738090 * dT,
+          0.145384923188325069727524825977071194859203467568236523866582 * dT,
+         -0.0782942710351670777553986729725692447252077047239160551335016* dT,
+         -0.114503299361098912184303164290554670970133218405658122674674 * dT);
+        felders[12].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(12,mDT,dT) then
+          continue;
+
+        felders[13].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],felders[6],felders[7],felders[8],felders[9],felders[10],felders[11],felders[12],
+          0.985115610164857280120041500306517278413646677314195559520529 * dT,
+          0.330885963040722183948884057658753173648240154838402033448632 * dT,
+          0.489662957309450192844507011135898201178015478433790097210790 * dT,
+         -1.37896486574843567582112720930751902353904327148559471526397  * dT,
+         -0.861164195027635666673916999665534573351026060987427093314412 * dT,
+          5.78428813637537220022999785486578436006872789689499172601856  * dT,
+          3.28807761985103566890460615937314805477268252903342356581925  * dT,
+         -2.38633905093136384013422325215527866148401465975954104585807  * dT,
+         -3.25479342483643918654589367587788726747711504674780680269911  * dT,
+         -2.16343541686422982353954211300054820889678036420109999154887  * dT);
+        felders[13].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(13,mDT,dT) then
+          continue;
+
+        felders[14].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[4],felders[6],felders[7],felders[8],felders[9],felders[10],felders[11],felders[12],felders[13],
+          0.895080295771632891049613132336585138148156279241561345991710 * dT,
+          0.197966831227192369068141770510388793370637287463360401555746 * dT,
+         -0.0729547847313632629185146671595558023015011608914382961421311* dT,
+         -0.851236239662007619739049371445966793289359722875702227166105 * dT,
+          0.398320112318533301719718614174373643336480918103773904231856 * dT,
+          3.63937263181035606029412920047090044132027387893977804176229  * dT,
+          1.54822877039830322365301663075174564919981736348973496313065  * dT,
+         -2.12221714704053716026062427460427261025318461146260124401561  * dT,
+         -1.58350398545326172713384349625753212757269188934434237975291  * dT,
+         -1.71561608285936264922031819751349098912615880827551992973034  * dT,
+         -0.0244036405750127452135415444412216875465593598370910566069132* dT);
+        felders[14].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(14,mDT,dT) then
+          continue;
+
+        felders[15].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],felders[5],felders[7],felders[13],felders[14],
+         -0.915176561375291440520015019275342154318951387664369720564660 * dT,
+          1.45453440217827322805250021715664459117622483736537873607016  * dT,
+         -0.777333643644968233538931228575302137803351053629547286334469 * dT,
+         -0.0910895662155176069593203555807484200111889091770101799647985* dT,
+          0.0910895662155176069593203555807484200111889091770101799647985* dT,
+          0.777333643644968233538931228575302137803351053629547286334469 * dT);
+        felders[15].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(15,mDT,dT) then
+          continue;
+
+        felders[16].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[15],
+          0.1                                                            * dT,
+         -0.157178665799771163367058998273128921867183754126709419409654 * dT,
+          0.157178665799771163367058998273128921867183754126709419409654 * dT);
+        felders[16].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(16,mDT,dT) then
+          continue;
+
+        felders[17].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],felders[3],felders[5],felders[6],felders[7],felders[8],felders[9],
+          felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],
+          0.181781300700095283888472062582262379650443831463199521664945 * dT,
+          0.675                                                          * dT,
+          0.342758159847189839942220553413850871742338734703958919937260 * dT,
+          0.259111214548322744512977076191767379267783684543182428778156 * dT,
+         -0.358278966717952089048961276721979397739750634673268802484271 * dT,
+         -1.04594895940883306095050068756409905131588123172378489286080  * dT,
+          0.930327845415626983292300564432428777137601651182965794680397 * dT,
+          1.77950959431708102446142106794824453926275743243327790536000  * dT,
+          0.1                                                            * dT,
+         -0.282547569539044081612477785222287276408489375976211189952877 * dT,
+         -0.159327350119972549169261984373485859278031542127551931461821 * dT,
+         -0.145515894647001510860991961081084111308650130578626404945571 * dT,
+         -0.259111214548322744512977076191767379267783684543182428778156 * dT,
+         -0.342758159847189839942220553413850871742338734703958919937260 * dT,
+         -0.675                                                          * dT);
+        felders[17].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(17,mDT,dT) then
+          continue;
+
+        felders[1-aktuelleFelder].liKo(
+          felders[aktuelleFelder],
+          felders[aktuelleFelder],
+          felders[2],
+          felders[3],
+          felders[5],
+          felders[7],
+          felders[9],
+          felders[10],
+          felders[11],
+          felders[12],
+          felders[13],
+          felders[14],
+          felders[15],
+          felders[16],
+          felders[17],
+          dT/30,
+          dT/40,
+          dT/30,
+          dT/20,
+          dT/25,
+          0.189237478148923490158306404106012326238162346948625830327194 * dT,
+          0.277429188517743176508360262560654340428504319718040836339472 * dT,
+          0.277429188517743176508360262560654340428504319718040836339472 * dT,
+          0.189237478148923490158306404106012326238162346948625830327194 * dT,
+         -dT/25,
+         -dT/20,
+         -dT/30,
+         -dT/40,
+         -dT/30
+        );
+      end;
+      zfRungeKuttaZwoelf: begin  // Quelle:  http://sce.uhcl.edu/rungekutta/rk1210.txt
+        felders[2].liKo(felders[aktuelleFelder],felders[aktuelleFelder],dT*0.2);
+        felders[2].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(2,mDT,dT) then
+          continue;
+
+        felders[3].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],
+         -0.216049382716049382716049382716049382716049382716049382716049 * dT,
+          0.771604938271604938271604938271604938271604938271604938271605 * dT);
+        felders[3].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(3,mDT,dT) then
+          continue;
+
+        felders[4].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],
+          dT/4.8,
+          0.625 * dT);
+        felders[4].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(4,mDT,dT) then
+          continue;
+
+        felders[5].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[4],
+          0.193333333333333333333333333333333333333333333333333333333333 * dT,
+          0.22                                                           * dT,
+         -0.08                                                           * dT);
+        felders[5].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(5,mDT,dT) then
+          continue;
+
+        felders[6].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],
+          0.1 * dT,
+          0.4 * dT,
+          0.5 * dT);
+        felders[6].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(6,mDT,dT) then
+          continue;
+
+        felders[7].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],felders[6],
+          0.103364471650010477570395435690481791543342708330349879244197 * dT,
+          0.124053094528946761061581889237115328211074784955180298044074 * dT,
+          0.483171167561032899288836480451962508724109257517289177302380 * dT,
+         -0.0387530245694763252085681443767620580395733302341368038804290* dT);
+        felders[7].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(7,mDT,dT) then
+          continue;
+
+        felders[8].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[5],felders[6],felders[7],
+          0.124038261431833324081904585980175168140024670698633612292480 * dT,
+          0.217050632197958486317846256953159942875916353757734167684657 * dT,
+          0.0137455792075966759812907801835048190594443990939408530842918* dT,
+         -0.0661095317267682844455831341498149531672668252085016565917546* dT);
+        felders[8].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(8,mDT,dT) then
+          continue;
+
+        felders[9].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],
+          0.0914774894856882983144991846980432197088832099976660100090486 * dT,
+         -0.00544348523717469689965754944144838611346156873847009178068318* dT,
+          0.0680716801688453518578515120895103863112751730758794372203952 * dT,
+          0.408394315582641046727306852653894780093303185664924644551239  * dT);
+        felders[9].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(9,mDT,dT) then
+          continue;
+
+        felders[10].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],
+          0.0890013652502551018954509355423841780143232697403434118692699 * dT,
+          0.00499528226645532360197793408420692800405891149406814091955810* dT,
+          0.397918238819828997341739603001347156083435060931424970826304  * dT,
+          0.427930210752576611068192608300897981558240730580396406312359  * dT,
+         -0.0865117637557827005740277475955029103267246394128995965941585 * dT);
+        felders[10].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(10,mDT,dT) then
+          continue;
+
+        felders[11].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],felders[10],
+          0.0695087624134907543112693906409809822706021061685544615255758 * dT,
+          0.129146941900176461970759579482746551122871751501482634045487  * dT,
+          1.53073638102311295076342566143214939031177504112433874313011   * dT,
+          0.577874761129140052546751349454576715334892100418571882718036  * dT,
+         -0.951294772321088980532340837388859453930924498799228648050949  * dT,
+         -0.408276642965631951497484981519757463459627174520978426909934  * dT);
+        felders[11].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(11,mDT,dT) then
+          continue;
+
+        felders[12].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],felders[10],felders[11],
+          0.0444861403295135866269453507092463581620165501018684152933313  * dT,
+         -0.00380476867056961731984232686574547203016331563626856065717964 * dT,
+          0.0106955064029624200721262602809059154469206077644957399593972  * dT,
+          0.0209616244499904333296674205928919920806734650660039898074652  * dT,
+         -0.0233146023259321786648561431551978077665337818756053603898847  * dT,
+          0.00263265981064536974369934736325334761174975280887405725010964 * dT,
+          0.00315472768977025060103545855572111407955208306374459723959783 * dT);
+        felders[12].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(12,mDT,dT) then
+          continue;
+
+        felders[13].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[9],felders[10],felders[11],felders[12],
+          0.0194588815119755475588801096525317761242073762016273186231215    * dT,
+          0.0000678512949171812509306121653452367476194364781259165332321534 * dT,
+         -0.0000429795859049273623271005330230162343568863387724883603675550 * dT,
+          0.0000176358982260285155407485928953302139937553442829975734148981 * dT,
+          0.0653866627415027051009595231385181033549511358787382098351924    * dT);
+        felders[13].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(13,mDT,dT) then
+          continue;
+
+        felders[14].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[9],felders[10],felders[11],felders[12],felders[13],
+          0.206836835664277105916828174798272361078909196043446411598231   * dT,
+          0.0166796067104156472828045866664696450306326505094792505215514  * dT,
+         -0.00879501563200710214457024178249986591130234990219959208704979 * dT,
+          0.00346675455362463910824462315246379209427513654098596403637231 * dT,
+         -0.861264460105717678161432562258351242030270498966891201799225   * dT,
+          0.908651882074050281096239478469262145034957129939256789178785   * dT);
+        felders[14].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(14,mDT,dT) then
+          continue;
+
+        felders[15].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[9],felders[10],felders[11],felders[12],felders[13],felders[14],
+          0.0203926084654484010091511314676925686038504449562413004562382  * dT,
+          0.0869469392016685948675400555583947505833954460930940959577347  * dT,
+         -0.0191649630410149842286436611791405053287170076602337673587681  * dT,
+          0.00655629159493663287364871573244244516034828755253746024098838 * dT,
+          0.0987476128127434780903798528674033899738924968006632201445462  * dT,
+          0.00535364695524996055083260173615567408717110247274021056118319 * dT,
+          0.301167864010967916837091303817051676920059229784957479998077   * dT);
+        felders[15].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(15,mDT,dT) then
+          continue;
+
+        felders[16].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[9],felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],
+          0.228410433917778099547115412893004398779136994596948545722283  * dT,
+         -0.498707400793025250635016567442511512138603770959682292383042  * dT,
+          0.134841168335724478552596703792570104791700727205981058201689  * dT,
+         -0.0387458244055834158439904226924029230935161059142806805674360 * dT,
+         -1.27473257473474844240388430824908952380979292713250350199641   * dT,
+          1.43916364462877165201184452437038081875299303577911839630524   * dT,
+         -0.214007467967990254219503540827349569639028092344812795499026  * dT,
+          0.958202417754430239892724139109781371059908874605153648768037  * dT);
+        felders[16].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(16,mDT,dT) then
+          continue;
+
+        felders[17].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[9],felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],
+          2.00222477655974203614249646012506747121440306225711721209798   * dT,
+          2.06701809961524912091954656438138595825411859673341600679555   * dT,
+          0.623978136086139541957471279831494466155292316167021080663140  * dT,
+         -0.0462283685500311430283203554129062069391947101880112723185773 * dT,
+         -8.84973288362649614860075246727118949286604835457092701094630   * dT,
+          7.74257707850855976227437225791835589560188590785037197433615   * dT,
+         -0.588358519250869210993353314127711745644125882130941202896436  * dT,
+         -1.10683733362380649395704708016953056176195769617014899442903   * dT,
+         -0.929529037579203999778397238291233214220788057511899747507074  * dT);
+        felders[17].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(17,mDT,dT) then
+          continue;
+
+        felders[18].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],
+          felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],felders[17],
+          3.13789533412073442934451608989888796808161259330322100268310   * dT,
+          0.129146941900176461970759579482746551122871751501482634045487  * dT,
+          1.53073638102311295076342566143214939031177504112433874313011   * dT,
+          0.577874761129140052546751349454576715334892100418571882718036  * dT,
+          5.42088263055126683050056840891857421941300558851862156403363   * dT,
+          0.231546926034829304872663800877643660904880180835945693836936  * dT,
+          0.0759292995578913560162301311785251873561801342333194895292058 * dT,
+        -12.3729973380186513287414553402595806591349822617535905976253    * dT,
+          9.85455883464769543935957209317369202080367765721777101906955   * dT,
+          0.0859111431370436529579357709052367772889980495122329601159540 * dT,
+         -5.65242752862643921117182090081762761180392602644189218673969   * dT,
+         -1.94300935242819610883833776782364287728724899124166920477873   * dT,
+         -0.128352601849404542018428714319344620742146491335612353559923  * dT);
+        felders[18].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(18,mDT,dT) then
+          continue;
+
+        felders[19].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[6],felders[7],felders[8],felders[9],
+          felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],felders[17],felders[18],
+          1.38360054432196014878538118298167716825163268489922519995564    * dT,
+          0.00499528226645532360197793408420692800405891149406814091955810 * dT,
+          0.397918238819828997341739603001347156083435060931424970826304   * dT,
+          0.427930210752576611068192608300897981558240730580396406312359   * dT,
+         -1.30299107424475770916551439123047573342071475998399645982146    * dT,
+          0.661292278669377029097112528107513072734573412294008071500699   * dT,
+         -0.144559774306954349765969393688703463900585822441545655530145   * dT,
+         -6.96576034731798203467853867461083919356792248105919255460819    * dT,
+          6.65808543235991748353408295542210450632193197576935120716437    * dT,
+         -1.66997375108841486404695805725510845049807969199236227575796    * dT,
+          2.06413702318035263832289040301832647130604651223986452170089    * dT,
+         -0.674743962644306471862958129570837723192079875998405058648892   * dT,
+         -0.00115618834794939500490703608435907610059605754935305582045729 * dT,
+         -0.00544057908677007389319819914241631024660726585015012485938593 * dT);
+        felders[19].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(19,mDT,dT) then
+          continue;
+
+        felders[20].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[5],felders[6],felders[7],felders[9],
+          felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],felders[17],felders[18],felders[19],
+          0.951236297048287669474637975894973552166903378983475425758226      * dT,
+          0.217050632197958486317846256953159942875916353757734167684657      * dT,
+          0.0137455792075966759812907801835048190594443990939408530842918     * dT,
+         -0.0661095317267682844455831341498149531672668252085016565917546     * dT,
+          0.152281696736414447136604697040747131921486432699422112099617      * dT,
+         -0.337741018357599840802300793133998004354643424457539667670080      * dT,
+         -0.0192825981633995781534949199286824400469353110630787982121133     * dT,
+         -3.68259269696866809932409015535499603576312120746888880201882       * dT,
+          3.16197870406982063541533528419683854018352080342887002331312       * dT,
+         -0.370462522106885290716991856022051125477943482284080569177386      * dT,
+         -0.0514974200365440434996434456698127984941168616474316871020314     * dT,
+         -0.000829625532120152946787043541792848416659382675202720677536554   * dT,
+          0.00000279801041419278598986586589070027583961355402640879503213503 * dT,
+          0.0418603916412360287969841020776788461794119440689356178942252     * dT,
+          0.279084255090877355915660874555379649966282167560126269290222      * dT);
+        felders[20].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(20,mDT,dT) then
+          continue;
+
+        felders[21].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[4],felders[5],felders[6],felders[8],
+          felders[10],felders[11],felders[18],felders[19],felders[20],
+          0.103364471650010477570395435690481791543342708330349879244197  * dT,
+          0.124053094528946761061581889237115328211074784955180298044074  * dT,
+          0.483171167561032899288836480451962508724109257517289177302380  * dT,
+         -0.0387530245694763252085681443767620580395733302341368038804290 * dT,
+         -0.438313820361122420391059788940960176420682836652600698580091  * dT,
+         -0.218636633721676647685111485017151199362509373698288330593486  * dT,
+         -0.0312334764394719229981634995206440349766174759626578122323015 * dT,
+          0.0312334764394719229981634995206440349766174759626578122323015 * dT,
+          0.218636633721676647685111485017151199362509373698288330593486  * dT,
+          0.438313820361122420391059788940960176420682836652600698580091  * dT);
+        felders[21].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(21,mDT,dT) then
+          continue;
+
+        felders[22].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[4],felders[7],felders[8],
+          felders[10],felders[11],felders[18],felders[19],felders[20],felders[21],
+          0.193333333333333333333333333333333333333333333333333333333333  * dT,
+          0.22                                                            * dT,
+         -0.08                                                            * dT,
+          0.0984256130499315928152900286856048243348202521491288575952143 * dT,
+         -0.196410889223054653446526504390100417677539095340135532418849  * dT,
+          0.436457930493068729391826122587949137609670676712525034763317  * dT,
+          0.0652613721675721098560370939805555698350543810708414716730270 * dT,
+         -0.0652613721675721098560370939805555698350543810708414716730270 * dT,
+         -0.436457930493068729391826122587949137609670676712525034763317  * dT,
+          0.196410889223054653446526504390100417677539095340135532418849  * dT,
+         -0.0984256130499315928152900286856048243348202521491288575952143 * dT);
+        felders[22].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(22,mDT,dT) then
+          continue;
+
+        felders[23].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],felders[5],felders[7],felders[21],
+          felders[22],
+         -0.216049382716049382716049382716049382716049382716049382716049 * dT,
+          0.771604938271604938271604938271604938271604938271604938271605 * dT,
+         -0.666666666666666666666666666666666666666666666666666666666667 * dT,
+         -0.390696469295978451446999802258495981249099665294395945559163 * dT,
+          0.390696469295978451446999802258495981249099665294395945559163 * dT,
+          0.666666666666666666666666666666666666666666666666666666666667 * dT);
+        felders[23].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(23,mDT,dT) then
+          continue;
+
+        felders[24].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[3],felders[23],
+          0.2                                                            * dT,
+         -0.164609053497942386831275720164609053497942386831275720164609 * dT,
+          0.164609053497942386831275720164609053497942386831275720164609 * dT);
+        felders[24].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(24,mDT,dT) then
+          continue;
+
+        felders[25].liKo(felders[aktuelleFelder],felders[aktuelleFelder],felders[2],felders[3],felders[5],felders[7],
+          felders[8],felders[9],felders[10],felders[11],felders[12],felders[13],felders[14],felders[15],felders[16],
+          felders[17],felders[18],felders[19],felders[20],felders[21],felders[22],felders[23],felders[24],
+          1.47178724881110408452949550989023611293535315518571691939396  * dT,
+          0.7875                                                         * dT,
+          0.421296296296296296296296296296296296296296296296296296296296 * dT,
+          0.291666666666666666666666666666666666666666666666666666666667 * dT,
+          0.348600717628329563206854421629657569274689947367847465753757 * dT,
+          0.229499544768994849582890233710555447073823569666506700662510 * dT,
+          5.79046485790481979159831978177003471098279506036722411333192  * dT,
+          0.418587511856506868874073759426596207226461447604248151080016 * dT,
+          0.307039880222474002649653817490106690389251482313213999386651 * dT,
+         -4.68700905350603332214256344683853248065574415794742040470287  * dT,
+          3.13571665593802262152038152399873856554395436199962915429076  * dT,
+          1.40134829710965720817510506275620441055845017313930508348898  * dT,
+         -5.52931101439499023629010306005764336421276055777658156400910  * dT,
+         -0.853138235508063349309546894974784906188927508039552519557498 * dT,
+          0.103575780373610140411804607167772795518293914458500175573749 * dT,
+         -0.140474416950600941142546901202132534870665923700034957196546 * dT,
+         -0.418587511856506868874073759426596207226461447604248151080016 * dT,
+         -0.229499544768994849582890233710555447073823569666506700662510 * dT,
+         -0.348600717628329563206854421629657569274689947367847465753757 * dT,
+         -0.291666666666666666666666666666666666666666666666666666666667 * dT,
+         -0.421296296296296296296296296296296296296296296296296296296296 * dT,
+         -0.7875                                                         * dT);
+        felders[25].berechneAbleitungen(dT/2,dX,iDT,iDX,pDNMax);
+
+        if pruefeMaxDT(25,mDT,dT) then
+          continue;
+
+
+        felders[1-aktuelleFelder].liKo(
+          felders[aktuelleFelder],
+          felders[aktuelleFelder],
+          felders[2],
+          felders[3],
+          felders[5],
+          felders[7],
+          felders[8],
+          felders[10],
+          felders[11],
+          felders[13],
+          felders[14],
+          felders[15],
+          felders[16],
+          felders[17],
+          felders[18],
+          felders[19],
+          felders[20],
+          felders[21],
+          felders[22],
+          felders[23],
+          felders[24],
+          felders[25],
+          0.0238095238095238095238095238095238095238095238095238095238095 * dT,
+          0.0234375                                                       * dT,
+          0.03125                                                         * dT,
+          0.0416666666666666666666666666666666666666666666666666666666667 * dT,
+          0.05                                                            * dT,
+          0.05                                                            * dT,
+          0.1                                                             * dT,
+          0.0714285714285714285714285714285714285714285714285714285714286 * dT,
+          0.138413023680782974005350203145033146748813640089941234591267  * dT,
+          0.215872690604931311708935511140681138965472074195773051123019  * dT,
+          0.243809523809523809523809523809523809523809523809523809523810  * dT,
+          0.215872690604931311708935511140681138965472074195773051123019  * dT,
+          0.138413023680782974005350203145033146748813640089941234591267  * dT,
+         -0.0714285714285714285714285714285714285714285714285714285714286 * dT,
+         -0.1                                                             * dT,
+         -0.05                                                            * dT,
+         -0.05                                                            * dT,
+         -0.0416666666666666666666666666666666666666666666666666666666667 * dT,
+         -0.03125                                                         * dT,
+         -0.0234375                                                       * dT,
+          0.0238095238095238095238095238095238095238095238095238095238095 * dT
+        );
+      end;
+      zfRungeKuttaVierzehn: begin   // Quelle:  http://sce.uhcl.edu/rungekutta/rk1412.txt
+      end;
     end{of case};
 
     break;
@@ -1205,6 +1704,18 @@ begin
           Zeitverfahren:=zfRungeKuttaVier;
           continue;
         end;
+        if s='runge-Kutta-10' then begin
+          Zeitverfahren:=zfRungeKuttaZehn;
+          continue;
+        end;
+        if s='runge-Kutta-12' then begin
+          Zeitverfahren:=zfRungeKuttaZwoelf;
+          continue;
+        end;
+        if s='runge-Kutta-14' then begin
+          Zeitverfahren:=zfRungeKuttaVierzehn;
+          continue;
+        end;
         if s='euler-Vorwärts' then begin
           Zeitverfahren:=zfEulerVorwaerts;
           continue;
@@ -1372,6 +1883,12 @@ begin
       pro.schreibe('Iteration mittels Runge-Kutta-3/8');
     zfRungeKuttaVier:
       pro.schreibe('Iteration mittels Runge-Kutta-4');
+    zfRungeKuttaZehn:
+      pro.schreibe('Iteration mittels Runge-Kutta-10');
+    zfRungeKuttaZwoelf:
+      pro.schreibe('Iteration mittels Runge-Kutta-12');
+    zfRungeKuttaVierzehn:
+      pro.schreibe('Iteration mittels Runge-Kutta-14');
     else
       pro.schreibe('Iteration mittels unbekanntem Verfahren');
   end{of case};
diff --git a/Plasmapropagation.lpi b/Plasmapropagation.lpi
index 28ad15a..c722825 100644
--- a/Plasmapropagation.lpi
+++ b/Plasmapropagation.lpi
@@ -32,7 +32,7 @@
         <LaunchingApplication PathPlusParams="/usr/bin/screen -T 'Lazarus Run Output' -e $(LazarusDir)/tools/runwait.sh $(TargetCmdLine)"/>
       </local>
     </RunParams>
-    <Units Count="4">
+    <Units Count="5">
       <Unit0>
         <Filename Value="Plasmapropagation.lpr"/>
         <IsPartOfProject Value="True"/>
@@ -49,6 +49,10 @@
         <Filename Value="input.plap"/>
         <IsPartOfProject Value="True"/>
       </Unit3>
+      <Unit4>
+        <Filename Value="linearkombination.inc"/>
+        <IsPartOfProject Value="True"/>
+      </Unit4>
     </Units>
   </ProjectOptions>
   <CompilerOptions>
diff --git a/Plasmapropagation.lps b/Plasmapropagation.lps
index e1cfd0c..3a563d0 100644
--- a/Plasmapropagation.lps
+++ b/Plasmapropagation.lps
@@ -3,25 +3,25 @@
   <ProjectSession>
     <Version Value="9"/>
     <BuildModes Active="Default"/>
-    <Units Count="12">
+    <Units Count="13">
       <Unit0>
         <Filename Value="Plasmapropagation.lpr"/>
         <IsPartOfProject Value="True"/>
-        <TopLine Value="11"/>
         <CursorPos X="34" Y="11"/>
-        <UsageCount Value="164"/>
+        <UsageCount Value="173"/>
         <Loaded Value="True"/>
       </Unit0>
       <Unit1>
         <Filename Value="Physikunit.pas"/>
         <IsPartOfProject Value="True"/>
+        <IsVisibleTab Value="True"/>
         <EditorIndex Value="1"/>
-        <TopLine Value="76"/>
-        <CursorPos X="60" Y="110"/>
-        <FoldState Value=" T3kf0-4 pigkU0A5 pjDjb084]9Ija0M3]94jY09[I43jO067[I5S0J1]9akG0U2 poOpJ0D2 T0\1Pc071'"/>
-        <UsageCount Value="105"/>
+        <TopLine Value="691"/>
+        <CursorPos X="46" Y="802"/>
+        <FoldState Value=" T3lM0-4 pigkU0A5 pjDjb084]9Ija09[943kG07[944jN0#nP p0xM0U2 pogpb0D2 T0~dPc071V"/>
+        <UsageCount Value="114"/>
         <Bookmarks Count="1">
-          <Item0 Y="1031"/>
+          <Item0 Y="1530"/>
         </Bookmarks>
         <Loaded Value="True"/>
       </Unit1>
@@ -31,23 +31,22 @@
         <EditorIndex Value="-1"/>
         <TopLine Value="20"/>
         <CursorPos X="22" Y="31"/>
-        <UsageCount Value="67"/>
+        <UsageCount Value="76"/>
       </Unit2>
       <Unit3>
         <Filename Value="input.plap"/>
         <IsPartOfProject Value="True"/>
-        <IsVisibleTab Value="True"/>
-        <EditorIndex Value="2"/>
-        <CursorPos Y="5"/>
-        <UsageCount Value="66"/>
+        <EditorIndex Value="3"/>
+        <CursorPos X="18" Y="4"/>
+        <UsageCount Value="75"/>
         <Loaded Value="True"/>
         <DefaultSyntaxHighlighter Value="None"/>
       </Unit3>
       <Unit4>
         <Filename Value="input.epost"/>
-        <EditorIndex Value="3"/>
+        <EditorIndex Value="4"/>
         <CursorPos X="32" Y="21"/>
-        <UsageCount Value="66"/>
+        <UsageCount Value="70"/>
         <Loaded Value="True"/>
         <DefaultSyntaxHighlighter Value="None"/>
       </Unit4>
@@ -57,14 +56,14 @@
         <TopLine Value="53"/>
         <CursorPos Y="53"/>
         <FoldState Value=" T3i905B pj0jV034 piaj60U2-"/>
-        <UsageCount Value="20"/>
+        <UsageCount Value="19"/>
       </Unit5>
       <Unit6>
         <Filename Value="../units/lowlevelunit.pas"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="4"/>
         <CursorPos X="86" Y="23"/>
-        <UsageCount Value="10"/>
+        <UsageCount Value="9"/>
       </Unit6>
       <Unit7>
         <Filename Value="../units/mystringlistunit.pas"/>
@@ -72,155 +71,165 @@
         <TopLine Value="367"/>
         <CursorPos X="17" Y="390"/>
         <FoldState Value=" T3i3075 piZjD0WQ"/>
-        <UsageCount Value="11"/>
+        <UsageCount Value="10"/>
       </Unit7>
       <Unit8>
         <Filename Value="../epost/werteunit.pas"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="950"/>
         <CursorPos X="30" Y="1054"/>
-        <UsageCount Value="8"/>
+        <UsageCount Value="7"/>
       </Unit8>
       <Unit9>
         <Filename Value="../epost/typenunit.pas"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="347"/>
         <CursorPos X="62" Y="358"/>
-        <UsageCount Value="8"/>
+        <UsageCount Value="7"/>
       </Unit9>
       <Unit10>
         <Filename Value="../units/systemunit.pas"/>
         <EditorIndex Value="-1"/>
         <CursorPos X="3" Y="79"/>
-        <UsageCount Value="8"/>
+        <UsageCount Value="7"/>
       </Unit10>
       <Unit11>
         <Filename Value="/usr/lib/fpc/src/rtl/inc/objpash.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="232"/>
         <CursorPos X="23" Y="192"/>
-        <UsageCount Value="8"/>
+        <UsageCount Value="7"/>
       </Unit11>
+      <Unit12>
+        <Filename Value="linearkombination.inc"/>
+        <IsPartOfProject Value="True"/>
+        <EditorIndex Value="2"/>
+        <TopLine Value="26"/>
+        <CursorPos X="21" Y="182"/>
+        <UsageCount Value="23"/>
+        <Loaded Value="True"/>
+      </Unit12>
     </Units>
     <JumpHistory Count="30" HistoryIndex="29">
       <Position1>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="121" Column="45" TopLine="98"/>
+        <Caret Line="124" Column="171" TopLine="97"/>
       </Position1>
       <Position2>
-        <Filename Value="Physikunit.pas"/>
-        <Caret Line="837" Column="13" TopLine="806"/>
+        <Filename Value="linearkombination.inc"/>
+        <Caret Line="3" Column="36"/>
       </Position2>
       <Position3>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="843" Column="10" TopLine="806"/>
+        <Caret Line="708" Column="47" TopLine="362"/>
       </Position3>
       <Position4>
-        <Filename Value="Physikunit.pas"/>
-        <Caret Line="835" Column="63" TopLine="806"/>
+        <Filename Value="linearkombination.inc"/>
+        <Caret Line="5" Column="16"/>
       </Position4>
       <Position5>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="121" Column="79" TopLine="112"/>
+        <Caret Line="590" Column="32" TopLine="377"/>
       </Position5>
       <Position6>
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diff --git a/input.plap b/input.plap
index b061987..b1adc5f 100644
--- a/input.plap
+++ b/input.plap
@@ -1,7 +1,10 @@
 # Parameterdatei für Plasmapropagation
 
 allgemein
-  runge-Kutta-3/8
+#  runge-Kutta-14
+  runge-Kutta-12
+#  runge-Kutta-10
+#  runge-Kutta-3/8
 #  runge-Kutta-4
 #  euler-Vorwärts
   ortsschritt    10^-2 * λ
diff --git a/linearkombination.inc b/linearkombination.inc
new file mode 100644
index 0000000..2d6a27d
--- /dev/null
+++ b/linearkombination.inc
@@ -0,0 +1,186 @@
+
+// Werte werden auf (in1 + \sum_i faki * ini') gesetzt
+
+procedure tWertePunkt.liKo(in1,in2
+{$IFDEF lkA3},in3
+{$IFDEF lkA4},in4
+{$IFDEF lkA5},in5
+{$IFDEF lkA6},in6
+{$IFDEF lkA7},in7
+{$IFDEF lkA8},in8
+{$IFDEF lkA9},in9
+{$IFDEF lkA10},in10
+{$IFDEF lkA11},in11
+{$IFDEF lkA12},in12
+{$IFDEF lkA14},in13,in14
+{$IFDEF lkA15},in15
+{$IFDEF lkA16},in16
+{$IFDEF lkA22},in17,in18,in19,in20,in21,in22
+{$IFDEF lkA23},in23
+{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}: tWertePunkt;
+fak2
+{$IFDEF lkA3},fak3
+{$IFDEF lkA4},fak4
+{$IFDEF lkA5},fak5
+{$IFDEF lkA6},fak6
+{$IFDEF lkA7},fak7
+{$IFDEF lkA8},fak8
+{$IFDEF lkA9},fak9
+{$IFDEF lkA10},fak10
+{$IFDEF lkA11},fak11
+{$IFDEF lkA12},fak12
+{$IFDEF lkA14},fak13,fak14
+{$IFDEF lkA15},fak15
+{$IFDEF lkA16},fak16
+{$IFDEF lkA22},fak17,fak18,fak19,fak20,fak21,fak22
+{$IFDEF lkA23},fak23
+{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}: extended);
+var
+  emF: tEMFeldInhalt;
+  maF: tMaterieFeldInhalt;
+  i:   longint;
+begin
+(*  tEMFeldInhalt = (
+      efA,efAX,efAY,efAZ,
+      efDAXDT,efDAYDT,efDAZDT,
+      efDPhiDX
+    ); *)
+  for emF:=efAX to efDPhiDX do // alles außer efA, welchen Ableitung ja nicht berechnet wurde
+    emWerte[emF,false]:=
+      in1.emWerte[emF,false]
+      + fak2  * in2.emWerte[emF,true]  {$IFDEF lkA3}
+      + fak3  * in3.emWerte[emF,true]  {$IFDEF lkA4}
+      + fak4  * in4.emWerte[emF,true]  {$IFDEF lkA5}
+      + fak5  * in5.emWerte[emF,true]  {$IFDEF lkA6}
+      + fak6  * in6.emWerte[emF,true]  {$IFDEF lkA7}
+      + fak7  * in7.emWerte[emF,true]  {$IFDEF lkA8}
+      + fak8  * in8.emWerte[emF,true]  {$IFDEF lkA9}
+      + fak9  * in9.emWerte[emF,true]  {$IFDEF lkA10}
+      + fak10 * in10.emWerte[emF,true] {$IFDEF lkA11}
+      + fak11 * in11.emWerte[emF,true] {$IFDEF lkA12}
+      + fak12 * in12.emWerte[emF,true] {$IFDEF lkA14}
+      + fak13 * in13.emWerte[emF,true]
+      + fak14 * in14.emWerte[emF,true] {$IFDEF lkA15}
+      + fak15 * in15.emWerte[emF,true] {$IFDEF lkA16}
+      + fak16 * in16.emWerte[emF,true] {$IFDEF lkA22}
+      + fak17 * in17.emWerte[emF,true]
+      + fak18 * in18.emWerte[emF,true]
+      + fak19 * in19.emWerte[emF,true]
+      + fak20 * in20.emWerte[emF,true]
+      + fak21 * in21.emWerte[emF,true]
+      + fak22 * in22.emWerte[emF,true] {$IFDEF lkA23}
+      + fak23 * in23.emWerte[emF,true]
+      {$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF};
+
+(*  tMaterieFeldInhalt = (
+      mfN,mfDPsiDX,
+      mfP,mfPX,mfPY,mfPZ,
+      mfGamma,mfIGamma
+    ); *)
+  for i:=0 to length(matWerte)-1 do // siehe oben
+    for maF:=mfN to mfDPsiDX do
+      matWerte[i,maF,false]:=
+        in1.matWerte[i,maF,false]
+        + fak2  * in2.matWerte[i,maF,true]  {$IFDEF lkA3}
+        + fak3  * in3.matWerte[i,maF,true]  {$IFDEF lkA4}
+        + fak4  * in4.matWerte[i,maF,true]  {$IFDEF lkA5}
+        + fak5  * in5.matWerte[i,maF,true]  {$IFDEF lkA6}
+        + fak6  * in6.matWerte[i,maF,true]  {$IFDEF lkA7}
+        + fak7  * in7.matWerte[i,maF,true]  {$IFDEF lkA8}
+        + fak8  * in8.matWerte[i,maF,true]  {$IFDEF lkA9}
+        + fak9  * in9.matWerte[i,maF,true]  {$IFDEF lkA10}
+        + fak10 * in10.matWerte[i,maF,true] {$IFDEF lkA11}
+        + fak11 * in11.matWerte[i,maF,true] {$IFDEF lkA12}
+        + fak12 * in12.matWerte[i,maF,true] {$IFDEF lkA14}
+        + fak13 * in13.matWerte[i,maF,true]
+        + fak14 * in14.matWerte[i,maF,true] {$IFDEF lkA15}
+        + fak15 * in15.matWerte[i,maF,true] {$IFDEF lkA16}
+        + fak16 * in16.matWerte[i,maF,true] {$IFDEF lkA22}
+        + fak17 * in17.matWerte[i,maF,true]
+        + fak18 * in18.matWerte[i,maF,true]
+        + fak19 * in19.matWerte[i,maF,true]
+        + fak20 * in20.matWerte[i,maF,true]
+        + fak21 * in21.matWerte[i,maF,true]
+        + fak22 * in22.matWerte[i,maF,true] {$IFDEF lkA23}
+        + fak23 * in23.matWerte[i,maF,true]
+        {$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF};
+end;
+
+// Werte werden auf (in1 + \sum_i faki * ini') gesetzt
+
+procedure tFelder.liKo(in1,in2
+{$IFDEF lkA3},in3
+{$IFDEF lkA4},in4
+{$IFDEF lkA5},in5
+{$IFDEF lkA6},in6
+{$IFDEF lkA7},in7
+{$IFDEF lkA8},in8
+{$IFDEF lkA9},in9
+{$IFDEF lkA10},in10
+{$IFDEF lkA11},in11
+{$IFDEF lkA12},in12
+{$IFDEF lkA14},in13,in14
+{$IFDEF lkA15},in15
+{$IFDEF lkA16},in16
+{$IFDEF lkA22},in17,in18,in19,in20,in21,in22
+{$IFDEF lkA23},in23
+{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}: tFelder;
+fak2
+{$IFDEF lkA3},fak3
+{$IFDEF lkA4},fak4
+{$IFDEF lkA5},fak5
+{$IFDEF lkA6},fak6
+{$IFDEF lkA7},fak7
+{$IFDEF lkA8},fak8
+{$IFDEF lkA9},fak9
+{$IFDEF lkA10},fak10
+{$IFDEF lkA11},fak11
+{$IFDEF lkA12},fak12
+{$IFDEF lkA14},fak13,fak14
+{$IFDEF lkA15},fak15
+{$IFDEF lkA16},fak16
+{$IFDEF lkA22},fak17,fak18,fak19,fak20,fak21,fak22
+{$IFDEF lkA23},fak23
+{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}: extended);
+var
+  i: longint;
+begin
+  for i:=0 to length(inhalt)-1 do
+    inhalt[i].liKo(
+      in1.inhalt[i],in2.inhalt[i]
+      {$IFDEF lkA3},in3.inhalt[i]
+      {$IFDEF lkA4},in4.inhalt[i]
+      {$IFDEF lkA5},in5.inhalt[i]
+      {$IFDEF lkA6},in6.inhalt[i]
+      {$IFDEF lkA7},in7.inhalt[i]
+      {$IFDEF lkA8},in8.inhalt[i]
+      {$IFDEF lkA9},in9.inhalt[i]
+      {$IFDEF lkA10},in10.inhalt[i]
+      {$IFDEF lkA11},in11.inhalt[i]
+      {$IFDEF lkA12},in12.inhalt[i]
+      {$IFDEF lkA14},in13.inhalt[i],in14.inhalt[i]
+      {$IFDEF lkA15},in15.inhalt[i]
+      {$IFDEF lkA16},in16.inhalt[i]
+      {$IFDEF lkA22},in17.inhalt[i],in18.inhalt[i],in19.inhalt[i],in20.inhalt[i],in21.inhalt[i],in22.inhalt[i]
+      {$IFDEF lkA23},in23.inhalt[i]
+      {$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF},
+      fak2
+      {$IFDEF lkA3},fak3
+      {$IFDEF lkA4},fak4
+      {$IFDEF lkA5},fak5
+      {$IFDEF lkA6},fak6
+      {$IFDEF lkA7},fak7
+      {$IFDEF lkA8},fak8
+      {$IFDEF lkA9},fak9
+      {$IFDEF lkA10},fak10
+      {$IFDEF lkA11},fak11
+      {$IFDEF lkA12},fak12
+      {$IFDEF lkA14},fak13,fak14
+      {$IFDEF lkA15},fak15
+      {$IFDEF lkA16},fak16
+      {$IFDEF lkA22},fak17,fak18,fak19,fak20,fak21,fak22
+      {$IFDEF lkA23},fak23
+      {$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF}{$ENDIF});
+end;
+
+
diff --git a/rk108.txt b/rk108.txt
new file mode 100644
index 0000000..2374007
--- /dev/null
+++ b/rk108.txt
@@ -0,0 +1,187 @@
+               THE COEFFICIENTS OF RK10(8)  TO 60 DIGITS

+            using the notation of Fehlberg, Bettis, Horn, et alia

+

+

+  k	         a[k]

+

+  0    0.000000000000000000000000000000000000000000000000000000000000

+  1    0.100000000000000000000000000000000000000000000000000000000000

+  2    0.539357840802981787532485197881302436857273449701009015505500

+  3    0.809036761204472681298727796821953655285910174551513523258250

+  4    0.309036761204472681298727796821953655285910174551513523258250

+  5    0.981074190219795268254879548310562080489056746118724882027805

+  6    0.833333333333333333333333333333333333333333333333333333333333

+  7    0.354017365856802376329264185948796742115824053807373968324184

+  8    0.882527661964732346425501486979669075182867844268052119663791

+  9    0.642615758240322548157075497020439535959501736363212695909875

+ 10    0.357384241759677451842924502979560464040498263636787304090125

+ 11    0.117472338035267653574498513020330924817132155731947880336209

+ 12    0.833333333333333333333333333333333333333333333333333333333333

+ 13    0.309036761204472681298727796821953655285910174551513523258250

+ 14    0.539357840802981787532485197881302436857273449701009015505500

+ 15    0.100000000000000000000000000000000000000000000000000000000000

+ 16    1.00000000000000000000000000000000000000000000000000000000000

+

+

+  k	         c[k]

+

+  0    0.0333333333333333333333333333333333333333333333333333333333333

+  1    0.0250000000000000000000000000000000000000000000000000000000000

+  2    0.0333333333333333333333333333333333333333333333333333333333333

+  3    0.000000000000000000000000000000000000000000000000000000000000

+  4    0.0500000000000000000000000000000000000000000000000000000000000

+  5    0.000000000000000000000000000000000000000000000000000000000000

+  6    0.0400000000000000000000000000000000000000000000000000000000000

+  7    0.000000000000000000000000000000000000000000000000000000000000

+  8    0.189237478148923490158306404106012326238162346948625830327194

+  9    0.277429188517743176508360262560654340428504319718040836339472

+ 10    0.277429188517743176508360262560654340428504319718040836339472

+ 11    0.189237478148923490158306404106012326238162346948625830327194

+ 12   -0.0400000000000000000000000000000000000000000000000000000000000

+ 13   -0.0500000000000000000000000000000000000000000000000000000000000

+ 14   -0.0333333333333333333333333333333333333333333333333333333333333

+ 15   -0.0250000000000000000000000000000000000000000000000000000000000

+ 16    0.0333333333333333333333333333333333333333333333333333333333333

+

+

+ k     j	  ß[k,j] 

+

+ 1    0    0.100000000000000000000000000000000000000000000000000000000000

+ 2    0   -0.915176561375291440520015019275342154318951387664369720564660

+ 2    1    1.45453440217827322805250021715664459117622483736537873607016

+ 3    0    0.202259190301118170324681949205488413821477543637878380814562

+ 3    1    0.000000000000000000000000000000000000000000000000000000000000

+ 3    2    0.606777570903354510974045847616465241464432630913635142443687

+ 4    0    0.184024714708643575149100693471120664216774047979591417844635

+ 4    1    0.000000000000000000000000000000000000000000000000000000000000

+ 4    2    0.197966831227192369068141770510388793370637287463360401555746

+ 4    3   -0.0729547847313632629185146671595558023015011608914382961421311

+ 5    0    0.0879007340206681337319777094132125475918886824944548534041378

+ 5    1    0.000000000000000000000000000000000000000000000000000000000000

+ 5    2    0.000000000000000000000000000000000000000000000000000000000000

+ 5    3    0.410459702520260645318174895920453426088035325902848695210406

+ 5    4    0.482713753678866489204726942976896106809132737721421333413261

+ 6    0    0.0859700504902460302188480225945808401411132615636600222593880

+ 6    1    0.000000000000000000000000000000000000000000000000000000000000

+ 6    2    0.000000000000000000000000000000000000000000000000000000000000

+ 6    3    0.330885963040722183948884057658753173648240154838402033448632

+ 6    4    0.489662957309450192844507011135898201178015478433790097210790

+ 6    5   -0.0731856375070850736789057580558988816340355615025188195854775

+ 7    0    0.120930449125333720660378854927668953958938996999703678812621

+ 7    1    0.000000000000000000000000000000000000000000000000000000000000

+ 7    2    0.000000000000000000000000000000000000000000000000000000000000

+ 7    3    0.000000000000000000000000000000000000000000000000000000000000

+ 7    4    0.260124675758295622809007617838335174368108756484693361887839

+ 7    5    0.0325402621549091330158899334391231259332716675992700000776101

+ 7    6   -0.0595780211817361001560122202563305121444953672762930724538856

+ 8    0    0.110854379580391483508936171010218441909425780168656559807038

+ 8    1    0.000000000000000000000000000000000000000000000000000000000000

+ 8    2    0.000000000000000000000000000000000000000000000000000000000000

+ 8    3    0.000000000000000000000000000000000000000000000000000000000000

+ 8    4    0.000000000000000000000000000000000000000000000000000000000000

+ 8    5   -0.0605761488255005587620924953655516875526344415354339234619466

+ 8    6    0.321763705601778390100898799049878904081404368603077129251110

+ 8    7    0.510485725608063031577759012285123416744672137031752354067590

+ 9    0    0.112054414752879004829715002761802363003717611158172229329393

+ 9    1    0.000000000000000000000000000000000000000000000000000000000000

+ 9    2    0.000000000000000000000000000000000000000000000000000000000000

+ 9    3    0.000000000000000000000000000000000000000000000000000000000000

+ 9    4    0.000000000000000000000000000000000000000000000000000000000000

+ 9    5   -0.144942775902865915672349828340980777181668499748506838876185

+ 9    6   -0.333269719096256706589705211415746871709467423992115497968724

+ 9    7    0.499269229556880061353316843969978567860276816592673201240332

+ 9    8    0.509504608929686104236098690045386253986643232352989602185060

+10    0    0.113976783964185986138004186736901163890724752541486831640341

+10    1    0.000000000000000000000000000000000000000000000000000000000000

+10    2    0.000000000000000000000000000000000000000000000000000000000000

+10    3    0.000000000000000000000000000000000000000000000000000000000000

+10    4    0.000000000000000000000000000000000000000000000000000000000000

+10    5   -0.0768813364203356938586214289120895270821349023390922987406384

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+

+

+ The estimate of the local truncation error is  (1/360)  h ( f(t1,x1)-f(t15,x15) )
\ No newline at end of file
diff --git a/rk1210.txt b/rk1210.txt
new file mode 100644
index 0000000..1155477
--- /dev/null
+++ b/rk1210.txt
@@ -0,0 +1,364 @@
+                     THE COEFFICIENTS OF RK12(10) TO 60 DIGITS

+             using the notation of Fehlberg, Bettis, Horn, et alia

+

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+

+ The estimate of the local truncation error is  (49/640)  h ( f(t1,x1)-f(t23,x23) )
\ No newline at end of file
diff --git a/rk1412.txt b/rk1412.txt
new file mode 100644
index 0000000..19ee14f
--- /dev/null
+++ b/rk1412.txt
@@ -0,0 +1,681 @@
+                     THE COEFFICIENTS OF RK14(12) TO 60 DIGITS

+             using the notation of Fehlberg,  Bettis,  Horn,  et alia.

+

+

+

+

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+32   22   0

+32   23   0

+32   24   0

+32   25   0

+32   26   0

+32   27   0

+32   28   0

+32   29   0

+32   30   0.492529543718026304422682049114021320200214681580657784719074

+32   31   0.750000000000000000000000000000000000000000000000000000000000

+33    0   0.111111111111111111111111111111111111111111111111111111111111

+33    1   0

+33    2  -0.222222222222222222222222222222222222222222222222222222222222

+33    3   0

+33    4   0

+33    5   0

+33    6   0

+33    7   0

+33    8   0

+33    9   0

+33   10   0

+33   11   0

+33   12   0

+33   13   0

+33   14   0

+33   15   0

+33   16   0

+33   17   0

+33   18   0

+33   19   0

+33   20   0

+33   21   0

+33   22   0

+33   23   0

+33   24   0

+33   25   0

+33   26   0

+33   27   0

+33   28   0

+33   29   0

+33   30   0

+33   31   0

+33   32   0.222222222222222222222222222222222222222222222222222222222222

+34    0   0.285835140388971558796088842163836414852927537894596466840753

+34    1   0.291666666666666666666666666666666666666666666666666666666667

+34    2   0.218750000000000000000000000000000000000000000000000000000000

+34    3   0

+34    4   0.164062500000000000000000000000000000000000000000000000000000

+34    5   0

+34    6   0.218194354945556658327188241581352107093288824322187941141516

+34    7   0.180392898478697766863635221946775437719620053641849228562435

+34    8   0

+34    9   0.205713839404845018859120755122929542277570094982808905393991

+34   10   0.242715791581770239970282927959446515762745971386670541948576

+34   11   0.246465780813629305833609291181891407799228103869305705137021

+34   12  -3.44991940790890824979834154601622662060370460614931644223924

+34   13   0.228875562160036081760729060738458584294220372552740218459295

+34   14   0.283290599702151415321527419056733335978436595493855789831434

+34   15   3.21085125837766640960131490544236787005557320332238705967955

+34   16  -0.223538777364845699920233756214162507964125230083674032084065

+34   17  -0.707121157204419073518727286207487212130091231955206160635271

+34   18   3.21123345150287080408174729202856500893260034443022374267639

+34   19   1.40954348309669766030414474301123175769045945573548986335553

+34   20  -0.151362053443742613121602276742518111090963026203676055891793

+34   21   0.372350574527014276454724080214619984397121028202148298716575

+34   22   0.252978746406361336722199907762141285915775728129414319261111

+34   23  -3.21085125837766640960131490544236787005557320332238705967955

+34   24  -0.283290599702151415321527419056733335978436595493855789831434

+34   25  -0.228875562160036081760729060738458584294220372552740218459295

+34   26  -0.246465780813629305833609291181891407799228103869305705137021

+34   27  -0.242715791581770239970282927959446515762745971386670541948576

+34   28  -0.205713839404845018859120755122929542277570094982808905393991

+34   29  -0.180392898478697766863635221946775437719620053641849228562435

+34   30  -0.218194354945556658327188241581352107093288824322187941141516

+34   31  -0.164062500000000000000000000000000000000000000000000000000000

+34   32  -0.218750000000000000000000000000000000000000000000000000000000

+34   33  -0.291666666666666666666666666666666666666666666666666666666667

+

+

+ The estimate of the local truncation error is  ( 1/1000 )  h ( f(t1,x1)-f(t33,x33) )