Journal de mathématiques appliquées et computationnelles

The Five-Point Difference Method Based on the K-Modes Cluster for Two-Dimensional Poisson Equations

Abstract

Jing Chen and Changzheng Xu

In this paper, we proposed a new method for the numerical solutions of a two-dimensional Poisson equation, where we used k-modes clustering algorithm to improve the standard five-point difference scheme. Numerical experiments have shown that the five-point difference method based on k-modes cluster is effective and efficient. The proposed new method not only reduces computing time remarkably, but also shows better performance in data storage and stability than the standard five-point difference scheme.