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

被引：0

作者：

Gupta, MM ^{[1
]}

Kouatchou, J ^{[1
]}

机构：

[1] George Washington Univ, Dept Math, Washington, DC 20052 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 1998年 / 14卷 / 05期

关键词：

finite difference approximations; Poisson equation; symbolic computation; Mathematica; three-dimensions;

D O I：

10.1002/(SICI)1098-2426(199809)14:5<593::AID-NUM4>3.0.CO;2-D

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 fourth-order 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. (C) 1998 John Wiley & Sons, Inc.

引用

页码：593 / 606

页数：14

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