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.
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页码：593 / 606
页数：14
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