The Solution of Pseudo-hyperbolic Telegraph Partial Differential Equation by Modified Double Laplace Method

Year 2022, Volume: 12 Issue: 1, 43 - 50, 15.06.2022

Mahmut Modanlı Fatma Şimşek

https://doi.org/10.31466/kfbd.929302

Cited By: 1

Abstract

In this study, the pseudo-hyperbolic telegraph partial differential equation depend on initial value conditions are investigated. For the exact solution of this equation, Modified double Laplace method is presented. This method is applied to the sample problem to obtain exact solution. The obtained this solution is showed by simulation. Thus, it was seen that the modified double Laplace method is convenient and suitable for the solution of this problem.

Keywords

Initial value problem, Exact solution, Modifiye double Laplace method, Pseudo-hyperbolic telegraph equation, Simulation

Pseudo-Hiperbolik Telegraf Kısmi Diferansiyel Denklemin Modifiye Çift Laplace Metodu ile Çözümü

Abstract

Bu araştırmada, başlangıç değer koşullarına bağlı pseudo-hiperbolik telegraf kısmi diferansiyel denklemi incelendi. Bu problemin tam çözümü için modifiye çift Laplace metodu verildi. Bu metot örnek problemlere uygulanarak tam çözüm elde edildi. Elde edilen bu çözüm simülasyonlarla gösterildi. Böylece modifiye çift Laplace metodunun bu problemin çözümü için elverişli ve uygun olduğu görüldü.

Keywords

Başlangıç değer problemi, tam çözüm, modifiye çift Laplace metodu, pseudo-hiperbolik telegraf denklemi, simülasyon.

References

• Borhanifar, A. ve Abazari, R., (2009). An unconditionally stable parallel difference scheme for telegraph equation. Mathematical Problems in Engineering, 2009.
• Lakestani, M. ve Saray, B. N., (2010). Numerical solution of telegraph equation using interpolating scaling functions. Computers & Mathematics with Applications, 60(7), 1964-1972.
• Latifizadeh, H., (2013). The sinc-collocation method for solving the telegraph equation. J. Comput. Inform, 1, 13-17. Arora, R., Singh, S., Singh, S., (2020). Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method. Mathematical Sciences, 14, 201-213.
• Arora, R. ve Singh, S., (2020). Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method. Mathematical Sciences, 14, 201-213.
• Kurt Bahşı, A. ve Yalçınbaş, S., (2016). A new algorithm for the numerical solution of telegraph equations by using Fibonacci polynomials. Mathematical and Computational Applications, 21(2), 15.
• Modanli, M. ve Akgül, A., (2017). Numerical solution of fractional telegraph differential equations by theta-method. The European Physical Journal Special Topics, 226(16), 3693-3703.
• Ozbag, F. ve Modanli, M. (2021). On the stability estimates and numerical solution of fractional order telegraph integro-differential equation. Physica Scripta, 96(9), 094008.
• Modanli, M., Ozbag, F. ve Akgül, A. (2022). Finite difference method for the fractional order pseudo telegraph integro-differential equation. Journal of Applied Mathematics and Computational Mechanics, 21(1), 41-54.
• Modanli, M., Abdulazeez, S. T. ve Husien, A. M., (2021). A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions. Numerical Methods for Partial Differential Equations, 37(3), 2235-2243.
• Gadain, H. E. (2018). Solving coupled pseudo-parabolic equation using a modified double Laplace decomposition method. Acta Mathematica Scientia, 38(1), 333-346.
• Eltayeb, H., Mesloub, S. ve Kılıçman, A., ( 2017). Application of double Laplace decomposition method to solve a singular one-dimensional pseudohyperbolic equation. Advances in Mechanical Engineering, 9(8), 1687814017716638.