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1、Matlab偏微分方程求解方法目录：§1FunctionSummaryonpage10-87§2InitialValueProblemsonpage10-88§3PDESolveronpage10-89§4IntegratorOptionsonpage10-92§5Examples”onpage10-93§1FunctionSummary1.1PDESolver”onpage10-871,2PDEHelperFunction”onpage10-871.3PDESolverThisistheMAT
2、LABPDEsolver.PDEInitial-BoundaryValueProblemSolverDescriptionpdepeSolveinitial-boundaryvalueproblemsforsystemsofparabolicandellipticPDEsinonespacevariableandtime.PDEHelperFunctionPDEHelperFunctionDescriptionpdevalEvaluatethenumericalsolutionofaPDEusi
3、ngtheoutputofpdepe§2InitialValueProblemspdepesolvessystemsofparabolicandellipticPDEsinonespatialvariablexandtimet,oftheform(10-2)ThePDEsholdfor.Theinterval[a,b]mustbefinite.mcanbe0,1,or2,correspondingtoslab,cylindrical,orsphericalsymmetry,respectivel
4、y.Ifm>0,thena≥0mustalsohold.InEquation10-2,isafluxtermandisasourceterm.Thefluxtermmustdependon.Thecouplingofthepartialderivativeswithrespecttotimeisrestrictedtomultiplicationbyadiagonalmatrix.Thediagonalelementsofthismatrixareeitheridenticallyzeroorp
5、ositive.Anelementthatisidenticallyzerocorrespondstoanellipticequationandotherwisetoaparabolicequation.Theremustbeatleastoneparabolicequation.Anelementofcthatcorrespondstoaparabolicequationcanvanishatisolatedvaluesofxiftheyaremeshpoints.Discontinuitie
6、sincand/orsduetomaterialinterfacesarepermittedprovidedthatameshpointisplacedateachinterface.Attheinitialtimet=t0,forallxthesolutioncomponentssatisfyinitialconditionsoftheform(10-3)Attheboundaryx=aorx=b,foralltthesolutioncomponentssatisfyaboundarycond
7、itionoftheform(10-4)q(x,t)isadiagonalmatrixwithelementsthatareeitheridenticallyzeroorneverzero.Notethattheboundaryconditionsareexpressedintermsofthefratherthanpartialderivativeofuwithrespecttox-.Also,ofthetwocoefficients,onlypcandependonu.§3PDESolver
8、3.1ThePDESolverTheMATLABPDEsolver,pdepe,solvesinitial-boundaryvalueproblemsforsystemsofparabolicandellipticPDEsintheonespacevariablexandtimet.Theremustbeatleastoneparabolicequationinthesystem.ThepdepesolverconvertsthePDEstoODEsusingasecond-orderaccur
