Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method

Abstract

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels, we use an appropriate variable transformations to convert the problem set into the unit interval [-1; 1], then the proposed method reduces the main problem to nonlinear system of algebraic equations. The convergence and errors analysis are discussed for both L^{infty} and L^{2}_{w} norms, we confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well known methods to illustrate the eficiency of this method.