New solutions of hyperbolic telegraph equation

Mustafa Inc, ,Department of Mathematics, Firat University, Elazig, Turkey, Mohammad Partohaghighi, Mehmet Ali Akinlar, Gerhard-Wilhelm Weber, ,Department of Mathematics, University of Bonab, Bonab, Iran, ,Dept. of Mathematical Engineering, Yildiz Technical Univ., Istanbul, Turkey, ,Poznan University of Technology, Poznan, Poland, IAM, Metu, Ankara, Turkey
2019 Journal of Dynamics & Games  
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
more » ... 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. 2020 Mathematics Subject Classification. Primary: 33E30, 34K28, 35G05, 35G15; Secondary: 65M22, 65J15.
doi:10.3934/jdg.2020029 fatcat:4m755kvsjvbs5ez75m4vy7u26q