A rational spectral collocation method for solving Fredholm integral equations on the whole line

Abstract

In this paper, a numerical method is proposed to solve a class of linear Fredholm integral equations on the whole line. The method is developed by means of mapped Gegenbauer rational functions. A special quadrature rule based on mapped Gegenbauer-Gauss points and weights is then utilised to evaluate the infinite integrals appeared in the scheme. Thus, the solution of the problem reduces to the solution of a simple system of algebraic equations. Convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method.