introductory-finite-difference-methods-for-pdes

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1、Introductory Finite Difference Methods for PDEs Professor D. M. Causon; Professor C. G. Mingham Download free books at ProfessorD.M.Causon&ProfessorC.G.MinghamIntroductoryFiniteDifferenceMethodsforPDEs2IntroductoryFiniteDifferenceMethodsforPDEs©2010Pr

2、ofessorD.M.Causon,ProfessorC.G.Mingham&VentusPublishingApSISBN978-87-7681-642-13IntroductoryFiniteDifferenceMethodsforPDEsContentsContentsPreface91.Introduction101.1PartialDifferentialEquations101.2SolutiontoaPartialDifferentialEquation101.3PDEModels1

3、11.4ClassificationofPDEs111.5DiscreteNotation151.6CheckingResults151.7Exercise1162.Fundamentals172.1Taylor’sTheorem172.2Taylor’sTheoremAppliedtotheFiniteDifferenceMethod(FDM)172.3SimpleFiniteDifferenceApproximationtoaDerivative182.4Example:SimpleFinit

4、eDifferenceApproximationstoaDerivative182.5ConstructingaFiniteDifferenceToolkit202.6SimpleExampleofaFiniteDifferenceScheme242.7PenandPaperCalculation(veryimportant)282.8Exercise2a322.9Exercise2b33Fast-trackyourcareerMastersinManagementStandoutfromthec

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7、entryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4IntroductoryFiniteDifferenceMethodsforPDEsContents3.

8、EllipticEquations343.1Introduction343.2FiniteDifferenceMethodforLaplace’sEquation343.3SettinguptheEquations373.4GridConvergence383.5DirectSolutionMethod383.6Exercise3a413.7IterativeSolutionMethods423.8JacobiIteration433.9Gauss-SeidelIteration4