Symbolic Derivation of
Finite Difference Approximations
for Three Dimensional Poisson Equation
Murli M. Gupta and Jules Kouatchou
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 is simple and can be used to obtain the finite difference approximations for other partial differential equations.