Numerical approximations of Fredholm integral equations with Abel kernel using Legendre and Chebychev polynomials

Abstract

In this study, Legendre and Chebychev collocation method are presented to solve numerically the Fredholm Integral Equations with Abel kernel. This method is based on replacement of the unknown function by truncated series of well known Legendre and Chebychev expansion of functions. This lead to a system of algebraic equations with Legendre and Chebychev coefficients. Thus, by solving the matrix equation, Legendre and Chebychev coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed technique.