An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1+1) Dimensions

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions. The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations. This is fulfilled by considering time variable as normal space variable. Under this scheme, there is no need to remove time-dependent variable during the whole solution process. Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method. We propose a simple shifted domain method, which can avoid the full-coefficient interpolation matrix easily. Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

Automated summary

This paper presents numerical solutions of the second-order one-dimensional hyperbolic telegraph equations using radial basis functions. The purpose is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations by treating the time variable as a normal space variable. The proposed shifted domain method can avoid the full-coefficient interpolation matrix easily, enhancing the numerical solution accuracy.