Barycentric Lagrange Interpolation Collocation Method For Solving Telegraph Equation

Telegraph equation arises in the research of propagation of electric signal and voltage signal in a cable of transmission line, also known as transmission line equation. It is a special kind of partial differential equation, which is difficult to obtain analytical solution and numerical solution is the main method. Therefore, it is of great significance to explore the rapid and accurate numerical algorithm methods for telegraph equation.The present paper proposes a numerical scheme to solve one and two-dimensional telegraph equation with constant and variable coefficients. The Barycentric Lagrange Interpolation collocation method is a new meshless method approximating the solution by using Barycentric Lagrange Interpolation functions, which also give results in discrete system equations. Without any form of grid division and solving the integral equation, it has characteristics of simple operation, high calculation accuracy. Therefore this paper mainly research content includes:(1) The calculation accuracy for Barycentric Lagrange Interpolation collocation method depends on the selection of interpolation nodes. On the space domain and time domain, Barycentric Lagrange Interpolation functions have been utilized for spatial, temporal variable and their derivatives using Chebyshev-Gauss-Lobatto collocation nodes.(2) We get the corresponding Interpolation functions into the initial-boundary value problem, which decomposed into differential operator through the Kronecker product. Meanwhile, it is convenient to acquire Interpolation scheme grasping the corresponding relation between the partial derivative of the differential equation and differential matrix of Barycentric Lagrange Interpolation.(3) The paper makes use of the symbol of the Kronecker product to simplify system equation into matrix form. For the matrix form of system equation on variable, coefficient matrix is diagonal matrix having the same order with the differential matrix, other operations do the same as constant coefficient equations. Method of substitution is adopted in this paper to solve the boundary conditions listing the applied process for the boundary conditions at the same time the concrete(4) Calculating programs of test examples are written by MATLAB software and the number sequence of computing nodes is important to program the initial conditions and boundary conditions. The efficacy and accuracy of the proposed method has been confirmed with numerical experiments.