Numerical Solution of Second-Order Linear Multidimensional Hyperbolic Telegraph Equation Using High-Order Compact Finite Difference Methods

The purpose of this study is to present a numerical method for solving the second-order linear multidimensional hyperbolic telegraph equation with boundary conditions in space and initial conditions in time. The main discretization theory is based on the implementation of the 4th, 6th, and 8th-order compact finite difference method in matrix form for spatial derivatives. The obtained system of linear ordinary differential equations in time is solved using the seventh-eighth-order continuous Runge-Kutta method. To analyze the convergence of the proposed method, the stability of the numerical method and simultaneously, the stability of the system obtained from the compact finite difference scheme are investigated. Moreover, the efficiency and accuracy of the present approach are illustrated by providing numerical examples and comparing the obtained results with some other techniques based on domain discretization.