Chebyshev spectral collocation method for system of nonlinear Volterra integral equations

Abstract

We investigate Chebyshev spectral collocation method for system of nonlinear Volterra integral equations. We choose Chebyshev Gauss points as collocation points, and approximate integral terms by Legendre Gauss quadrature formula. The provided convergence analysis shows that numerical errors decay exponentially, which is one of the most prominent features of spectral methods. Numerical experiments are carried out to confirm theoretical results. We have never seen any paper investigating the spectral method for the system of nonlinear Volterra integral equations (VIEs). The present method and corresponding convergence analysis would be useful in studying numerical methods for the system of integral equations and partial differential equations.