BLOCK UNIFICATION ALGORITHM FOR 2D AND 3D ELLIPTIC PDEs

T. A. BIALA, S. N. JATOR

Abstract


A continuous linear multistep method (LMM) is constructed and used to obtain a block linear multistep method (BLMM) of order 2. The BLMM is then extended on the entire interval of interest and combined as a block unification method to solve elliptic partial differential equations (PDEs)in two and three dimensions via the method of lines. In particular, the method is used to solve elliptic PDE by converting the PDE into a system of ordinary differential equations (ODEs) by replacing one of the spatial derivatives with the central difference method. The stability and convergence properties of the method are discussed. We have tested the accuracy of the BLMM on several numerical examples.

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