Numerical solution of special 2D Fredholm-Volterra integral equations using barycentric Gegenbauer interpolation collocation method

Abstract

In this paper, an efficient collocation method based on two dimensional barycentric Gegenbauer interpolation is used to solve a kind of special two dimensional Fredholm-Volterra integral equations (2D-FVIEs). The explicit barycentric weights for the Gegenbauer-Gauss nodes not only reduce the complicated calculation but also preserve the numerical stability. The combination of the barycentric interpolation and the Legendre-Gauss quadrature formula transforms the 2D-FVIEs into a system of discrete algebraic equations whose solution is a set of the nodal function values. The numerical experiments provide the maximum absolute error and the convergent order to assess the accuracy and the convergence of the method.