Applied Mathematical Sciences, Vol. 6, 2012, no. 34, 1655 – 1666 A New Method for Solving 3D Elliptic Problem with Dirichlet or Neumann Boundary Conditions Using Finite Difference Method J. Izadian ∗ and S. S. Jalalian Department of Mathematics, Faculty of Sciences, Mashad Branch, Islamic Azad University, Mashad, Iran. Jalal_Izadian@yahoo.com M. Jalili Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. Jalili.maryam@yahoo.com Abstract In this paper, a new algorithm for solving general three dimensional linear Elliptic types P.D.E.’s applying finite difference method is introduced. In this method, the boundary conditions are considered as auxiliary equations coupling with the main equations to constitute a system of linear equations, using suitable finite difference partial derivatives. The mesh points are also generated simply by proposed algorithm. This algorithm can perform numbering of mesh points, generating matrix coefficient, and right hand side vector by a special automatic procedure. Numerical experiments are presented to show performance, reliability and efficiency of proposed algorithm. Keywords: Elliptic equation, Neumann Boundary Conditions, Dirichlet conditions, Finite difference method