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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.. convergence.. Methods andconjugategradients.. of steepestdescent .. direction.. algorithm.. CG..866 TheInitialValueProblemforODE' .. solutions.. Equations .. canceof theLipschitzconstant .. LeVeque|AMath585{6 Notesiii7 Zero-Stability.}}}}

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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