SavedAdd your journal

Journals / Journal of Mathematical Sciences and Modelling / 2022 / Cilt: 5 - Sayı: 3

Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation

Mahmut MODANLI
Fatih ÖZBAĞ
Pages
92–98
Publication Date
2022-12-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It can be drawn that the established scheme is accurate and effective

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering.
📊
Key Findings & Data:As a result of the error analysis, the maximum norm errors tend to decrease as we increase the grid points.
💡
Conclusion & Impact:It can be drawn that the established scheme is accurate and effective
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Finite difference scheme · Telegraph equation · Pseudo-hyperbolic equation

Abstract

Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. Therefore, in this study, an initial-boundary value issue is proposed for the pseudo-hyperbolic telegraph equation. By operator method, converting the PDE to an ODE provides an exact answer to this problem. After that, the finite difference method is applied to construct first-order finite difference schemes to calculate approximate numerical solutions. The stability estimations of finite difference schemes are shown, as well as some numerical tests to check the correctness in comparison to the precise solution. The numerical solution is subjected to error analysis. As a result of the error analysis, the maximum norm errors tend to decrease as we increase the grid points. It can be drawn that the established scheme is accurate and effective

🔖

Cite This Article

MODANLI, M., ÖZBAĞ, F. (2022). Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling, Cilt: 5 - Sayı: 3, 92–98. https://ajindex.com/articles/869304

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. A. Din, Y. Li, F. M. Khan, Z. U. Khan, P. Liu, On analysis of fractional order mathematical model of Hepatitis B using Atangana-Baleanu Caputo (ABC) derivative, Fractals, 30(01) (2022), 2240017
  2. A. Din, Y. Li, T. Khan, G. Zaman, Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China, Chaos Solitons Fractals, 141 (2020), 110286
  3. P. Veeresha, M. Yavuz, C. Baishya, A computational approach for shallow water forced Korteweg-De Vries equation on critical flow over a hole with three fractional operators, Int. J. Optim. Control: Theor. Appl., 11(3) (2021), 52-67
  4. F. Özbağ, Numerical simulations of traveling waves in a counterflow filtration combustion model, Turk. J. Math., 46(4) (2022), 1424-1435
  5. L. Zada, R. Nawaz, K. S. Nisar, M. Tahir, M. Yavuz, New approximate-analytical solutions to partial differential equations via auxiliary function method, Partial Differ. Eq. Appl. Math., 4 (2021), 100045
  6. Z. Hammouch, M. Yavuz, N. Özdemir, Numerical solutions and synchronization of a variable-order fractional chaotic system, Math. Model. Numer. Simul. App., 1(1) (2021), 11-23
  7. H. Eltayeb, S. Mesloub, Y. T. Abdalla, A. Kilicman, A note on double conformable Laplace transform method and singular one dimensional conformable pseudo-hyperbolic equations, Mathematics, 7(10) (2019), 949
  8. S. V. Potapova, Boundary value problems for pseudo-hyperbolic equations with a variable time direction, J. Pure Appl. Math., 3(1) (2012), 75-91
  9. Y. Zhang, Y. Niu, D. Shi, Nonconforming H1 -Galerkin mixed finite element method for pseudo-hyperbolic equations, American J. Comp. Math., 2 (2012), 269-273
  10. Y. Liu, J. Wang, H. Li, W. Gao, S. He, A new splitting H1-Galerkin mixed method for pseudo-hyperbolic equations, Int. J. Math. Comp. Sci., 5(3) (2011), 1444-1449
  11. I. Fedotov, M.Y. Shatalov, J. Marais, Hyperbolic and pseudo-hyperbolic equations in the theory of vibration, Acta Mech., 227(11) (2016), 3315-3324
  12. G. Chen, Z. Yang, Initial value problem for a class of nonlinear pseudo-hyperbolic equations, Acta Math. App. Sinica, 9(2) (1993), 166-173
  13. P. A. Krutitskii, An initial-boundary value problem for the pseudo-hyperbolic equation of gravity-gyroscopic waves, J. Math. Kyoto Univ., 37(2) (1997), 343-365
  14. Z. Zhao, H. Li, A continuous Galerkin method for pseudo-hyperbolic equations with variable coefficients, J. Math. Anal. App., 473(2) (2019), 1053-1072
  15. M. Modanli, F. Özbağ, A. Akgülma, Finite d