Jacobi spectral method for the second-kind Volterra integral equations with a weakly singular kernel

The Jacobi spectral Galerkin method for Volterra integral equations of the second kind with a weakly singular kernel is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the Lωα,β2-norm and the L∞L∞-norm) will decay exponentially provided that the source function is sufficiently smooth. Numerical examples are given to illustrate theoretical results.