Numerical Solutions of Elliptic Partial Differential Equations

Abstract

Numerical techniques for the solution of two dimensional Elliptic partial differential equations such as Laplace and Poison equations were investigated. These types of differential equations have specific applications in physical and engineering models. The discrete approximation of both equations is based on finite difference method. In this article, five points finite difference approximation was used for two dimensional Laplace’s and Poisson’s equations. To solve the resulting finite difference approximation, basic iterative methods; Jacobi, GaussSeidel and Successive over Relaxation (SOR) have been used. Two model problems were solved and concluding remarks are presented.