diff options
| -rw-r--r-- | Physikunit.pas | 823 | ||||
| -rw-r--r-- | Plasmapropagation.lpi | 6 | ||||
| -rw-r--r-- | Plasmapropagation.lps | 133 | ||||
| -rw-r--r-- | input.plap | 5 | ||||
| -rw-r--r-- | linearkombination.inc | 186 | ||||
| -rw-r--r-- | rk108.txt | 187 | ||||
| -rw-r--r-- | rk1210.txt | 364 | ||||
| -rw-r--r-- | rk1412.txt | 681 |
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 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TopLine="872"/> + <Filename Value="linearkombination.inc"/> + <Caret Line="18" Column="50"/> </Position27> <Position28> <Filename Value="Physikunit.pas"/> - <Caret Line="88" Column="64" TopLine="64"/> + <Caret Line="638" Column="15" TopLine="596"/> </Position28> <Position29> <Filename Value="Physikunit.pas"/> - <Caret Line="597" TopLine="526"/> + <Caret Line="1519" TopLine="1497"/> </Position29> <Position30> <Filename Value="Physikunit.pas"/> - <Caret Line="811" Column="19" TopLine="778"/> + <Caret Line="134" Column="248" TopLine="110"/> </Position30> </JumpHistory> </ProjectSession> @@ -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]
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+
+
+ k c[k]
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+
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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) )
|