Approximate solution of a system of singular integral equations of the first kind by using Chebyshev polynomials

TL;DR

This paper presents a Chebyshev polynomial-based numerical method for solving systems of first-kind Cauchy singular integral equations on finite segments, including error estimation and numerical validation.

Contribution

It introduces a novel Chebyshev polynomial approach for these equations along with an error estimation technique, enhancing solution accuracy and computational efficiency.

Findings

The method effectively solves the integral equations.

Numerical results confirm the accuracy of the approach.

Error estimates align well with actual errors.

Abstract

The aim of the present work is to introduce a method based on Chebyshev polynomials for the numerical solution of a system of Cauchy type singular integral equations of the first kind on a finite segment. Moreover, an estimation error is computed for the approximate solution. Numerical results demonstrate effectiveness of the proposed method.