Open Access

ARTICLE

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

by Fuzhang Wang^1,2, Enran Hou^2,*, Imtiaz Ahmad³, Hijaz Ahmad⁴, Yan Gu⁵

1 College of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, 221018, China
2 College of Mathematics, Huaibei Normal University, Huaibei, 235000, China
3 Department of Mathematics, University of Swabi, Swabi, 25000, Pakistan
4 Department of Basic Sciences, University of Engineering and Technology, Peshawar, 25000, Pakistan
5 College of Mathematics, Qingdao University, Qingdao, 266071, China

* Corresponding Author: Enran Hou. Email:

(This article belongs to the Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 128(2), 687-698. https://doi.org/10.32604/cmes.2021.014739

Received 26 October 2020; Accepted 16 April 2021; Issue published 22 July 2021

Abstract

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.

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Citations