Barycentric rational interpolation collocation method for solving two-dimensional linear and nonlinear integro-differential equations

Abstract

Barycentric rational interpolation is characterized by excellent numerical stability, high approximation accuracy, and strong adaptability to node distribution. In this paper, we propose a high-precision barycentric rational interpolation collocation method to provide approximate solutions for both linear and nonlinear two-dimensional integro-differential equations (2D-IDEs) subject to specified boundary conditions. Firstly, the discrete scheme for 2D-IDEs is derived by employing the two-dimensional barycentric rational interpolation formula and the two-dimensional Gauss-Legendre numerical integration formula. Then, the error estimation of the approximate solution and the convergence of the method are analyzed. Finally, numerical examples are provided to validate the effectiveness and accuracy of the proposed method.