On the Approximate Solution of Integral Equations with Logarithmic Kernels Using the Third Kind of Chebyshev Polynomials

TL;DR

This paper introduces a new method using third kind Chebyshev polynomials to efficiently approximate solutions to second type Volterra integral equations with logarithmic kernels, demonstrating convergence and superior performance.

Contribution

The paper proposes a novel expansion procedure with third kind Chebyshev polynomials for solving integral equations with logarithmic kernels, including convergence analysis and comparative results.

Findings

Method shows high accuracy in examples

Convergence of the algorithm is established

Outperforms existing methods in efficiency

Abstract

An expansion procedure using third kind Chebyshev polynomials as base functions is suggested for solving second type Volterra integral equations with logarithmic kernels. The algorithm's convergence is studied and some illustrative examples are presented to show the method's efficiency and reliability, comparisons with other methods in the literature are made.