Legendre spectral Galerkin method for second-kind Volterra integral equations.

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L 2 norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]