Applied Mathematical Sciences, Vol. 6, 2012, no. 8, 369 – 380 New Method for Solving Poisson Equation on Irregular Domains J. Izadian and N. Karamooz Department of Mathematics, Faculty of Sciences Mashhad Branch,Islamic Azad University, Mashhad, Iran M. Jalili Department of Mathematics, Neyshabur Branch Islamic Azad University, Neyshabur, Iran Jalili.maryam@yahoo.com Abstract In this paper a new method for solving Poisson equation with Dirichlet conditions on non-rectangular domains is presented. For this purpose, two numerical differentiation methods are introduced for non-equidistant points. These two types of numerical differentiations are used for solving Poisson problems on irregular domains , with two types of meshes : irregular and semi-irregular. In this paper the numerical differentiation method applying non-equidistant points are introduced. The numerical results show the efficiency and performance of proposed method. Keywords: Poisson Equation , Dirichlet condition , Finite differences method (FDM), Irregular domains 1 Introduction One of the most important partial differential equations is Poisson equation that has great applications in science. There is a variety of papers related to this subject. This equation belong to elliptic PDE’s group. There are various numerical methods for solving these equations, FEM, BEM, etc. For a fundamental review of these methods one can refer to Ames [1], McDonough [3].