Symbolic Derivation of Finite Difference Approximations for the Three-Dimensional Poisson Equation -- from Wolfram Library Archive

Title

Symbolic Derivation of Finite Difference Approximations for the Three-Dimensional Poisson Equation

Authors

M. Gupta

J. Kouatchou

Journal / Anthology

Numerical Methods for Partial Differential Equations

Year:

1998

Volume:

Issue:

Page range:

593-606

Description

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.

Subjects

	Applied Mathematics > Numerical Methods
	Mathematics > Calculus and Analysis > Differential Equations

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