重心Lagrange插值配点法求解二维双曲电报方程

Barycentric Lagrange Interpolation Collocation Method for Two-dimensional Hyperbolic Telegraph Equation

提出一种求解二维双曲电报方程的高精度重心Lagrange插值配点法.采用重心Lagrange插值构造包含时间和空间变量的近似函数.在给定Chebyshev-Gauss-Lobatto节点上,将多变量重心Lagrange插值近似函数代入双曲电报方程及其定解条件,得到离散代数方程组.包含狄里克雷和诺依曼边界条件的数值算例表明,本文方法程序实现方便并具有高精度,可应用于求解高维问题.

We propose a numerical scheme for two-dimensional hyperbolic telegraph equation,in which Chebyshev-Gauss-Lobatto collocation nodes and approximate solutions with multi-variable barycentric Lagrange interpolation functions are used. Multi-variable barycentric Lagrange interpolation functions are given for spatial,temporal variable and their derivatives. Accuracy of the method is demonstrated with test examples with Dirichlet and Neumann boundary conditions. Numerical results are more accurate than numerical solutions in literatures. In additional,the method is easy to implement for multidimensional problems.