A New Method for Solving 3D Elliptic Problem with Dirichlet or Neumann Boundary Conditions Using Finite Difference Method

Abstract

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