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

Fuzhang Wang1,2, Enran Hou2,*, 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 this Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 128(2), 687-698.


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.


Cite This Article

Wang, F., Hou, E., Ahmad, I., Ahmad, H., Gu, Y. (2021). An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions. CMES-Computer Modeling in Engineering & Sciences, 128(2), 687–698.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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