Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant

It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation. However, classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order. In contrast with the classical rational interpolants, the generalized barycentric rational interpolants which depend linearly on the interpolated values, yield infinite smooth approximation with no poles in real numbers. In this paper, a numerical collocation approach, based on the generalized barycentric rational interpolation and Gaussian quadrature formula, was introduced to approximate the solution of Volterra-Fredholm integral equations. Three types of points in the solution domain are used as interpolation nodes. The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations. Moreover, integral equations with Runge’s function as an exact solution, no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.