Nadjafi, Jafar Saberi; Samadi, Omid Reza Navid; Tohidi, Emran Numerical solution of two-dimensional Volterra integral equations by spectral Galerkin method. (English) Zbl 1270.65079 J. Appl. Math. Bioinform. 1, No. 2, 159-174 (2011). 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. Cited in 9 Documents MSC: 65R20 Numerical methods for integral equations 45D05 Volterra integral equations 45G10 Other nonlinear integral equations Keywords:two-dimensional integral equations; spectral discontinuous Galerkin method; ultraspherical polynomials; numerical examples; Volterra integral equation; Gauss-Legendre quadrature rule PDFBibTeX XMLCite \textit{J. S. Nadjafi} et al., J. Appl. Math. Bioinform. 1, No. 2, 159--174 (2011; Zbl 1270.65079)