On the Numerical Solution for Two Dimensional Laplace Equation with Initial Boundary Conditions by using Finite Difference Methods

Abstract

In this study, Laplace partial differential equations with initial boundary conditions has been studied. A numerical method has been proposed for the solution of the IBVP Laplace equation. The technique based on finite difference methods. The stability of the difference schemes are guaranteed. Approximation solution of the problem was achieved. For testing the accuracy of the proposed method, two different initial boundary value problems are provided. Moreover, a comparison between the numerical solution and analytical solution has been done. MATLAB software implemented for calculation of absolute errors. Illustration graphs presented. It has been demonstrated that the results of the comparison guarantee the accuracy and reliability of the provided method.