Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations

Abstract

The barycentric form of Lagrange interpolant is attractive due to its stability, fast convergent rate, high precision and so on. In this paper, we applies an algorithm based on two dimensional extension of barycentric Lagrange interpolant for solving two dimensional integro-differential equations (2D-IDEs) numerically. First, the solution of the 2D-IDEs is replaced by the extended two dimensional barycentric Lagrange interpolant which is constructed by tensor product nodes, the set of differential operators is discretized by the differential matrix of barycentric interpolant, the double integral is approximated by an extended Gauss-type quadrature formula and the boundary conditions are treated by the substitute method. Then the solution of the 2D-IDEs is transformed into the solution of the corresponding system of algebraic equations. The error estimation and convergence analysis are also discussed. Last, several numerical examples are given to demonstrate the merits of the current method.