A meshless based method for solution of integral equations: Improving the error analysis

TL;DR

This paper presents an improved error analysis for a meshless collocation method using MLS approximation to solve integral equations, enhancing previous results and contributing to the theoretical understanding of such methods.

Contribution

It provides an improved error analysis for MLS-based collocation methods, advancing the theoretical framework for meshless solutions of integral equations.

Findings

Enhanced error bounds compared to previous analysis

Theoretical validation of MLS collocation accuracy

Extension of error analysis techniques to integral equations

Abstract

This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian of some parts of Chapter 2 of the author's PhD thesis in 2011.