book-2005-Practical Scientific Computing.pdf

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1、AMATH581PracticalScientificComputing∗J.NathanKutz†January4,2005AbstractThiscourseisasurveyofpracticalnumericalsolutiontechniquesforordinaryandpartialdifferentialequations.Emphasiswillbeontheimple-mentationofnumericalschemestopracticalproblemsintheengineeringandphysicalsciences.Me

2、thodsforpartialdifferentialequationswillin-cludefinitedifference,finiteelementandspectraltechniques.FullusewillbemadeofMATLABanditsprogrammingfunctionality.∗ThesenotesareintendedastheprimarysourceofinformationforAMATH581.Thenotesareimcompleteandmaycontainerrors.Anyotheruseasidefrom

3、classroompurposesandpersonalresearchpleasecontactmeatkutz@amath.washington.edu.cJ.N.Kutz,Autumn2003(Version1.1)†DepartmentofAppliedMathematics,Box352420,UniversityofWashington,Seattle,WA98195-2420(kutz@amath.washington.edu).1AMATH581(cJ.N.Kutz)2Contents1InitialandBoundaryValueP

4、roblemsofDifferentialEquations51.1Initialvalueproblems:Euler,Runge-KuttaandAdamsmethods51.2Erroranalysisfortime-steppingroutines..............121.3Boundaryvalueproblems:theshootingmethod..........171.4Implementationofshootingandconvergencestudies.......231.5Boundaryvalueproblems

5、:directsolveandrelaxation......282FiniteDifferenceMethods342.1Finitedifferencediscretization...................342.2DirectsolutionmethodsforAx=b.................392.3IterativesolutionmethodsforAx=b................442.4Fast-PoissonSolvers:theFourierTransform...........492.5Compari

6、sonofsolutiontechniquesforAx=b:rulesofthumb..522.6Overcomingcomputationaldifficulties...............573TimeandSpaceSteppingSchemes:MethodofLines613.1Basictime-steppingschemes.....................623.2Time-steppingschemes:explicitandimplicitmethods......663.3Stabilityanalysis.....

7、......................713.4Comparisonoftime-steppingschemes...............753.5Optimizingcomputationalperformance:rulesofthumb.....784SpectralMethods844.1Fast-FourierTransformsandCosine/Sinetransform.......844.2ChebychevPolynomialsandTransform..............884.3Spectralmethodim

8、plementation..................934.4Pseudo-spectraltech