SPECTRAL METHODS FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS

Abstract

In this paper we propose and analyze a spectral Jacobi - Collocation approximation for the linear Volterra integral equations of the second kind with weakly singular kernels. we consider the case when the underlying solutions of the volterra integral equations are sufficiently smooth. In this case, we provide a rigorous error analysis for proposed method, which shows that the numerical errors decay exponentially in the infinity norm and weighted Sobolev space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence.