Application of Lerch Polynomials to Approximate Solution of Singular Fredholm Integral Equations with Cauchy KernelApplication of Lerch Polynomials to Approximate Solution of Singular Fredholm Integral Equations with Cauchy Kernel

Abstract

In this paper, we develop an effective method based on Lerch polynomials to provide an approximate solution of various cases of Cauchy type singular integral equations. The method reduces the solution of given singular integral equation to the solution of a matrix equation corresponding to linear system of algebraic equations with unknown Lerch coefficients. Error estimation of the presented method is mentioned. Finally, several examples show the reliability and efficiently of the proposed method