Bulletin of the
Korean Mathematical Society BKMS

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations \linebreak (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^\infty$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

Keywords: spectral Galerkin methods, Jacobi polynomial, Volterra integral equations with weakly singular kernels

MSC numbers: Primary 65R20, 45J05, 65N12