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Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation

✍ Scribed by Murli M. Gupta; Jules Kouatchou

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 307 KB
Volume: 14
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199809)14:5<593::aid-num4>3.0.co;2-d

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✦ Synopsis

A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourthorder finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations.

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