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

M. Gupta
J. Kouatchou
Journal / Anthology

Numerical Methods for Partial Differential Equations
Year: 1998
Volume: 14
Issue: 5
Page range: 593-606

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.

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