IJPAM: Volume 7, No. 3 (2003)

A NUMERICAL TECHNIQUE FOR
THE 3-D POISSON EQUATION

Salwa K. Abd-El-Hafiz$^1$, Gamal A.F. Ismail$^2$, Berlant S. Matit$^3$
$^1$Department of Engineering Mathematics
Faculty of Engineering
Cairo University
Giza, EGYPT
e-mail: salwahafiz@link.net
$^{2,3}$Department of Applied Mathematics
Faculty for Girls
Ain Shams University
Asma Fahmy St. Heliopolis
Cairo, EGYPT
$^3$e-mail: berlantm@operamail.com


Abstract.In this paper,we solve the three-dimensional Poisson equation with Dirichlet boundary conditions. The Poisson equation is, first, discretized using the finite difference method. We choose an indexing strategy for the grid points, which is essential for the efficient solution of Poisson equation at all grid points. Then, an iterative method is used to solve the resulting linear system. Finally, we present an example that demonstrates the accuracy of the method.

Received: March 3, 2003

AMS Subject Classification: 65L12

Key Words and Phrases: Poisson equation, Dirichlet boundary conditions, discretization, finite difference, successive over relaxation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 3