Numerical solution of quadratic integral equations of Urysohn type on the half-line by using rational Legendre spectral method

Abstract

This paper presents a numerical method for the solution of quadratic integral equations of Urysohn type on the half-line. The main idea of this method is to reduce the Urysohn integral equation to a system of nonlinear algebraic equations by using a rational Legendre-collocation approximation (RLC). An order convergence analysis is provided. Numerical examples are presented to illustrate the accuracy and stability of the proposed method.