Mixed Neumann-Fourier expressions for solving integral equations

TL;DR

This paper introduces a novel approach combining Neumann and Fourier series to effectively approximate solutions of integral equations, demonstrating promising approximation qualities.

Contribution

It presents and investigates a new combined series method for solving integral equations, blending Neumann and Fourier series techniques.

Findings

Good approximation qualities observed

Effective for solving integral equations

Potential for further application and development

Abstract

While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short article presents and investigates this combination of approximating series.