×

Numerical solution of two-dimensional Volterra integral equations by spectral Galerkin method. (English) Zbl 1270.65079

Summary: 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.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite