Solving Poisson equations by the MN-curve approach

Abstract

In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is mathematically complicated and applies only to function interpolations. Here we aim at presenting an easily accessible approach to solving differential equations with the choice theory which proves to be successful, not only by its easy accessibility, but also by its striking accuracy and efficiency.