New solutions of hyperbolic telegraph equation

Date

2021-04-01

Author

İnç, Mustafa
Partohaghighi, Mohammad
Akınlar, Mehmet Ali
Weber, Gerhard-Wilhelm

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We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.

Subject Keywords

Hyperbolic telegraph equation, group preserving scheme, fictitious time integration method

URI

https://hdl.handle.net/11511/90744

Journal

JOURNAL OF DYNAMICS AND GAMES

DOI

https://doi.org/10.3934/jdg.2020029

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. İnç, M. Partohaghighi, M. A. Akınlar, and G.-W. Weber, “New solutions of hyperbolic telegraph equation,” JOURNAL OF DYNAMICS AND GAMES, pp. 129–138, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/90744.