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-rw-r--r--Physikunit.pas823
-rw-r--r--Plasmapropagation.lpi6
-rw-r--r--Plasmapropagation.lps133
-rw-r--r--input.plap5
-rw-r--r--linearkombination.inc186
-rw-r--r--rk108.txt187
-rw-r--r--rk1210.txt364
-rw-r--r--rk1412.txt681
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>
<Filename Value="Physikunit.pas"/>
- <Caret Line="861" TopLine="855"/>
+ <Caret Line="596" Column="14" TopLine="286"/>
</Position6>
<Position7>
<Filename Value="Physikunit.pas"/>
- <Caret Line="120" TopLine="120"/>
+ <Caret Line="590" TopLine="355"/>
</Position7>
<Position8>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="121" Column="59" TopLine="98"/>
+ <Filename Value="linearkombination.inc"/>
+ <Caret Line="48" Column="55" TopLine="13"/>
</Position8>
<Position9>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="851" TopLine="806"/>
+ <Filename Value="linearkombination.inc"/>
+ <Caret Line="82" Column="89" TopLine="45"/>
</Position9>
<Position10>
<Filename Value="Physikunit.pas"/>
- <Caret Line="911" Column="64" TopLine="879"/>
+ <Caret Line="608" Column="15" TopLine="523"/>
</Position10>
<Position11>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="913" Column="16" TopLine="897"/>
+ <Filename Value="linearkombination.inc"/>
+ <Caret Line="79" Column="45" TopLine="45"/>
</Position11>
<Position12>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="18" Column="77"/>
+ <Filename Value="linearkombination.inc"/>
+ <Caret Line="28"/>
</Position12>
<Position13>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="785" Column="44" TopLine="674"/>
+ <Filename Value="Plasmapropagation.lpr"/>
+ <Caret Line="11" Column="40" TopLine="11"/>
</Position13>
<Position14>
<Filename Value="Physikunit.pas"/>
- <Caret Line="915" Column="23" TopLine="883"/>
+ <Caret Line="1255" TopLine="1233"/>
</Position14>
<Position15>
<Filename Value="Physikunit.pas"/>
- <Caret Line="1072" Column="34" TopLine="981"/>
+ <Caret Line="1498" Column="77" TopLine="1465"/>
</Position15>
<Position16>
<Filename Value="Physikunit.pas"/>
- <Caret Line="1119" Column="48" TopLine="1087"/>
+ <Caret Line="1281" Column="80" TopLine="1269"/>
</Position16>
<Position17>
- <Filename Value="Physikunit.pas"/>
- <Caret Line="1123" Column="42" TopLine="1091"/>
+ <Filename Value="linearkombination.inc"/>
+ <Caret Line="140" Column="19" TopLine="108"/>
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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
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+ 7 0.000000000000000000000000000000000000000000000000000000000000
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+ 10 0.277429188517743176508360262560654340428504319718040836339472
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+ 12 -0.0400000000000000000000000000000000000000000000000000000000000
+ 13 -0.0500000000000000000000000000000000000000000000000000000000000
+ 14 -0.0333333333333333333333333333333333333333333333333333333333333
+ 15 -0.0250000000000000000000000000000000000000000000000000000000000
+ 16 0.0333333333333333333333333333333333333333333333333333333333333
+
+
+ k j ß[k,j]
+
+ 1 0 0.100000000000000000000000000000000000000000000000000000000000
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+ 2 1 1.45453440217827322805250021715664459117622483736537873607016
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diff --git a/rk1210.txt b/rk1210.txt
new file mode 100644
index 0000000..1155477
--- /dev/null
+++ b/rk1210.txt
@@ -0,0 +1,364 @@
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+ 24 23 -0.787500000000000000000000000000000000000000000000000000000000
+
+ 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.
+
+
+
+
+ k a[k]
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+
+
+ The estimate of the local truncation error is ( 1/1000 ) h ( f(t1,x1)-f(t33,x33) )