(有限差分法)Finite Difference Methods for__ D

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1、FiniteDierenceMethodsforDierentialEquationsRandallJ.LeVequeDRAFTVERSIONforuseinthecourseAMath585{586UniversityofWashingtonVersionofSeptember,2005WARNING:Thesenotesareincompleteandmaycontainerrors.Theyaremadeavailableprimarilyforstudentsinmycourses.Pleasecontactmeforotheruses.rjl@amath.washington.

2、educR.J.LeVeque,1998{20052cR.J.LeVeque,2004

3、UniversityofWashington

4、AMath585{6NotesContentsIBasicText11Finitedierenceapproximations31.1Truncationerrors........................................51.2Derivingnitedierenceapproximations...........................61.3Polynomialinterpolation..............

5、......................71.4Secondorderderivatives....................................71.5Higherorderderivatives....................................81.6Exercises............................................82BoundaryValueProblems112.1Theheatequation.......................................112.2Boundaryc

6、onditions......................................122.3Thesteady-stateproblem...................................122.4Asimplenitedierencemethod...............................132.5Localtruncationerror.....................................142.6Globalerror...........................................152.7S

7、tability.............................................152.8Consistency...........................................162.9Convergence...........................................162.10Stabilityinthe2-norm.....................................172.11Green'sfunctionsandmax-normstability.......................

8、...192.12Neumannboundaryconditions................................212.13Existenceanduniqueness...................................232.14Agenerallinearsecondorderequation............................242.15NonlinearEquations......................................262.15.1DiscretizationofthenonlinearBVP..

9、.......................272.15.2Nonconvergence....................................292.15.3Nonuniqueness.....................................292.15.4Accuracyonnonlinearequations...........................292.