General Discrete Scheme of Finite Difference Method Based on Node Set Vector for Two Dimensional Poisson Equation

Abstract

This paper presents a general discrete scheme of finite difference method based on node set vector for numerical computation of two dimensional Poisson equation, it firstly achieved the relationships between various derivatives by Poisson equation, then deduced simplification of truncated Taylor series by the relationships, based on the simplified expression, the paper analyzed the basic discrete scheme of any high order, investigated general scheme of interior node and boundary node, at last the paper conducted the comparisons of discrete scheme with other forms put forth in other paper, the results testified that the general discrete scheme of any order proposed by this paper is true.