Finite Difference Method with Dirichlet Problems of 2D Laplace’s Equation in Elliptic Domain

In this study finite difference method (FDM) is used with Dirichlet boundary conditions on rectangular domain to solve the 2D Laplace equation. The chosen body is elliptical, which is discretized into square grids. The finite difference method is applied for numerical differentiation of the observed example of rectangular domain with Dirichlet boundary conditions. The obtained numerical results arecompared with analytical solution. The obtained results show the efficiency of the FDM and settled with the obtained exact solution. The study objective is to check the accuracy of FDM for the numerical solutions of elliptical bodies of 2D Laplace equations. The study contributes to find the heat (temperature) distribution inside a regular rectangular elliptical discretized body