Study on the Fourth Order Discrete Scheme of Finite Difference Method Based on Node Set Vector for Two Dimensional Poisson Equation

Abstract

A novel fourth order discrete scheme of finite difference method based on node set vector for two dimensional Poisson equation is presented in this paper, in which key problems such as basic discrete scheme of this method, discrete scheme of interior node and boundary node are investigated profoundly, at last, a sample computation on a two dimensional domain of given distribution function is conducted by computer programs developed according to algorithms of this method, the emulating results testified that this fourth order discrete scheme is effective for numerical computation of two dimensional Poisson equation.