On the numerical solution of second order two-dimensional Laplace equations using the alternating-direction implicit method

Abstract

Abstract In this manuscript, we consider in detail numerical approach of solving Laplace’s equation in 2-dimensional region with given boundary values which is based on the Alternating Direction Implicit Method (ADI). This method was constructed using Taylor’s series expansion on the second order Laplace equation leading to a linear algebraic system. Solving the algebraic system, leads to the unknown coefficients of the basis function. The techniques of handling practical problems are considered in detail. The results obtained compared favorably with the results obtained from the Finite difference method constructed by Dhumal and Kiwne and the exact solution. Thus the ADI method can as well be used for the numerical solution of steady-state Laplace equations.