Error Estimates of a Symmetric Spectral Method for a Linear Volterra Integral Equation

A symmetric spectral method is applied to investigate the two-dimensional Volterra integral equation with weakly singular kernels and delays. In this work, solution of we considered assumed be sufficiently smooth so that can naturally. Employing three couples variable transformations, apply Gauss quadrature rule approximate delays obtain discretization. Then derive convergence results proposed approximation scheme. We show errors decay exponentially in both infinity norm weighted square norm. end, carry out numerical experiments verify theoretical results.