Numerical study of integer-order hyperbolic telegraph model arising in physical and related sciences

Published on Sep 1, 2020in European Physical Journal Plus3.911
· DOI :10.1140/EPJP/S13360-020-00784-Z
M. Abdel-Aty1
Estimated H-index: 1
 (Sohag University)
Source
Abstract
More recently, it is discovered in the field of applied sciences and engineering that the telegraph equation is better suited to model reaction-diffusion than the ordinary diffusion equation. In this article, the second-order hyperbolic telegraph equations are analyzed numerically by means of an efficient local differential quadrature method utilizing the radial basis functions. The explicit time integration technique is used to semi-discretize the model in the time direction, while the space derivatives are discretized by the proposed meshless procedure. To test the accuracy and capabilities of the method, five test problems are considered utilizing both rectangular and non-rectangular domains, which show that the proposed scheme solutions are converging extremely quick in comparison with the different existing numerical techniques in the recent literature.
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References53
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