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.

拉格朗日插值的重心形式具有稳定性，收敛速度快，精度高等优点。在本文中，我们将基于重心拉格朗日插值的二维扩展的算法用于二维求解二维积分微分方程（2D-IDE）。首先，用张量积节点构成的扩展的二维重心拉格朗日插值代替2D-IDEs的解，通过重心插值的微分矩阵离散化微分算子集，通过扩展将双积分近似高斯型正交公式和边界条件用替代法处理。然后将2D-IDE的解转换为相应代数方程组的解。还讨论了误差估计和收敛分析。最后，给出了几个数值例子来说明当前方法的优点。