Accession Number : ADA306919

Title :   Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation.

Descriptive Note : Contractor rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Abarbanel, Saul ; Ditkowski, Adi

PDF Url : ADA306919

Report Date : FEB 1996

Pagination or Media Count : 38

Abstract : An algorithm is presented which solves the multi-dimensional diffusion equation on complex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

Descriptors :   *ALGORITHMS, *PARTIAL DIFFERENTIAL EQUATIONS, TIME DEPENDENCE, TWO DIMENSIONAL, MATRICES(MATHEMATICS), GRIDS, ACCURACY, MESH, FINITE DIFFERENCE THEORY, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, NUMERICAL METHODS AND PROCEDURES, ASYMPTOTIC NORMALITY, EXTRAPOLATION.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE