Numerical Solution of Two-Dimensional Volterra Integral Equations by Spectral Galerkin Method

摘要

In this paper, we present ultraspherical spectral discontinuous Galerkin method for solving the two-dimensional volterra integral equation (VIE) of the second kind. The Gauss-Legendre quadrature rule is used to approximate the integral operator and the inner product based on the ultraspherical weights is implemented in the weak formulation. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. Moreover, a comparison is made with another numerical approach that is proposed recently for solving two-dimensional VIEs.