有限差分方法基础 (2).ppt

《有限差分方法基础 (2).ppt》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、1材料计算机数值模拟讲义TheFiniteDifferenceCalculus21、IntroductiontoNumericalMethods2、theTaylorSeries3、DifferenceCalculus3ThePurposeandPowerofNumericalMethodsaswellastheirLimitationsNumericalMethodsareaclassofmethodsforSolvingawidevarietyofMathematicalProblems:theElectronicComputershavebee

2、ninwidespreadusesincethemiddle1950’s;NumericalMethodsactuallypredateelectroniccomputersbymanyyears;NumericalMethodscameofagewiththeintroductionoftheElectronicComputer.4TheCombinationofNumericalMethodsanddigitalcomputershascreatedatoolofimmensepowerinMathematicalAnalyses:theNume

3、ricalMethodsarecapableofhandlingthenonlinearities,complexgeometries,andlargesystemsofcoupledequationswhicharenecessaryfortheaccuratesimulationofmanyrealphysicalsituations;NumericalMethodshavedisplacedclassicalmathematicalanalysisinmanyindustrialandresearchapplications;Numerical

4、MethodsaresoeasyandiexpensivetoemployandareoftenavailableasprepackagedPrograms.5Therearemanyproblemswhicharestillimpossible(insomecasesweshouldsay“impractical”)tosolveusingNumericalMethods:forsomeoftheseproblemsnoaccurateandcompletemathemeticalmodelhasyetbeenfound;Otherproblems

5、aresimplysoenourmousthattheirsolutionisbeyondpracticallimitsintermsofcurrentcomputertechnology;Ofcourse,theentirequestionofpracticalityisstronglydependentuponhowmuchoneiswillingtospend...6TostudyNumericalMethods:Nocomplexphysicalsituationcanbeexactlysimulatedbyamathematicalmode

6、l;Nonumericalmethodiscompletelytrouble-freeinallsituation;Nonumericalmethodiscompletelyerror-free;Nonumericalmethodisoptimalforallsituation.7ComputerlanguagestoNumericalMethods:“highlevel”computerlanguagesuchasFORTRAN,ALGOL,orBASIC;Compilertoconvert“highlevel”languagetomachinec

7、ode;ByfarthemostwidelyusedalgebraiclanguageforscientificpurposeisFORTRAN.Now,somelanguagesuchasMATLAB…8TheVerificationProblemtoNumericalAnalysis:Oneofthemostvitaandyetdifficulttaskswhichmustbecarriedoutinobtaininganumericalsolutiontoanyproblemistoverifythatthecomputerprogramand

8、thefinalsolutionarecorrect;Theverificationprocedurecan