Solving Poisson equations by the MN-curve approach

TL;DR

This paper introduces an accessible method using the MN-curve approach and shape parameter choice theory to efficiently and accurately solve Poisson equations with radial basis functions.

Contribution

It presents a simplified, effective approach to solving differential equations by applying the new MN-curve shape parameter choice theory, improving accessibility and performance.

Findings

High accuracy in solving Poisson equations

Efficient computational performance

Accessible methodology for differential equations

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.