A Modification on The Exponential Cubic B-spline for Numerical Simulation of Hyperbolic Telegraph Equations

Subject Areas : International Journal of Industrial Mathematics

احمدرضا حقیقی ¹ , فروزان رحیمیان ² , نسیم عسگری ³ , M. Roohi ⁴

1 - Department of Mathematics, Allameh Tabatabai University, Tehran, Iran.
2 - Department of Mathematics, Urmia University of Technology, Urmia, Iran.
3 - Department of Mathematics Islamic Azad University, Central Tehran Branch,Tehran, Iran.
4 - Department of Mathematics, School of Economics and Statistics, Guangzhou, China.

Received: 2022-02-18 Accepted : 2023-08-13 Published : 2023-07-01

Keywords: Telegraph equation (TE), Exponential modified, Differential. quadrature method, SSP-RK43, Cubic B-spline function,

Abstract :

In this paper the differential quadrature method is implemented to find numerical solution of two and three-dimensional telegraphic equations with Dirichlet and Neumann's boundary values. This technique is according to exponential cubic B-spline functions. So, a modification on the exponential cubic B- spline is applied in order to use as a basis function in the DQ method. Therefore, the Telegraph equation (TE) is altered to a system of ordinary differential equations (ODEs). The optimized form of Runge-Kutta scheme has been implemented by four-stage and three-order strong stability preserving (SSPRK43) to solve the resulting system of ODEs. We examined the correctness and applicability of this method by four examples of the TE.