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Finite Di erence Methods for Di erential Equations

FiniteDi erenceMethodsforDi erentialEquationsRandallJ. LeVequeDRAFTVERSION forusein thecourseAMath585{586 University of WashingtonVersionof September,2005 WARNING:Thesenotesareincompleteandmay in my R. J. LeVeque,1998{20052c LeVeque,2004|University of Washington|AMath585{6 NotesContentsIBasicText11 Finitedi .. nitedi erenceapproximations..82 .. simple nitedi erencemethod .. in the2-norm.. 'sfunctionsandmax-normstability .. generallinearsecondorderequation.. thenonlinearBVP.. re nement .. erencing..37iiiCONTENTS3 .. ve-point stencilfortheLaplacian.. Laplacian..484 .. basedonpolynomialinterpolation.. niteelement method .. spacedimensions..605 Iterative Methods .. matrixsplittingmethods.}}}

Finite Di erence Methods for Di erential Equations Randall J. LeVeque DRAFT VERSION for use in the course AMath 585{586 University of Washington Version of September, 2005

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