SYMBOLIC DERIVATION OF FINITE-DIFFERENCE APPROXIMATIONS FOR THE 3-DIMENSIONAL POISSON EQUATION

Authors
GUPTA MM KOUATCHOU J
Citation
Mm. Gupta et J. Kouatchou, SYMBOLIC DERIVATION OF FINITE-DIFFERENCE APPROXIMATIONS FOR THE 3-DIMENSIONAL POISSON EQUATION, Numerical methods for partial differential equations, 14(5), 1998, pp. 593-606
Citations number
13
Categorie Soggetti
Mathematics,Mathematics
Journal title
Numerical methods for partial differential equations → ACNP
ISSN journal
0749159X
Volume
14
Issue
5
Year of publication
1998
Pages
593 - 606
Database
ISI
SICI code
0749-159X(1998)14:5<593:SDOFAF>2.0.ZU;2-G
Abstract
A symbolic procedure for deriving various finite difference approximat ions for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation loca l solutions of the differential equation and obtain the standard secon d-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 di fference approximations for other partial differential equations. (C) 1998 John Wiley & Sons, Inc.