On Pseudo-spectral Method for Second-kind Weakly Singularvolterra Integral Equations with Smooth Solutions

The Jacobi pseudo-spectral Galerkin method for the weakly singular Volterra integral equations of the second kind with smooth solutions is proposed in this study. We provide a rigorous error analysis for the proposed method which indicates that the numerical errors (in the L super( 2)-norm and the L infinity -norm ) will decay exponentially provided that the source function is sufficiently smooth. Numerical examples are given to illustrate the theoretical results.