Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation

Mahmut Modanlı; Fatih Özbağ

doi:10.33187/jmsm.1132139

EN

Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph 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

Keywords

Finite difference scheme, Telegraph equation, Pseudo-hyperbolic equation, Stability

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mahmut Modanlı
0000-0002-7743-3512
Türkiye

Fatih Özbağ ^*
0000-0002-5456-4261
Türkiye

Publication Date

December 1, 2022

Submission Date

June 17, 2022

Acceptance Date

September 2, 2022

Published in Issue

Year 2022 Volume: 5 Number: 3

DOI

https://doi.org/10.33187/jmsm.1132139

IZ

https://izlik.org/JA56XD53JF

APA

Modanlı, M., & Özbağ, F. (2022). Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling, 5(3), 92-98. https://doi.org/10.33187/jmsm.1132139

AMA

1.Modanlı M, Özbağ F. Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2022;5(3):92-98. doi:10.33187/jmsm.1132139

Chicago

Modanlı, Mahmut, and Fatih Özbağ. 2022. “Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation”. Journal of Mathematical Sciences and Modelling 5 (3): 92-98. https://doi.org/10.33187/jmsm.1132139.

EndNote

Modanlı M, Özbağ F (December 1, 2022) Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling 5 3 92–98.

IEEE

[1]M. Modanlı and F. Özbağ, “Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation”, Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, pp. 92–98, Dec. 2022, doi: 10.33187/jmsm.1132139.

ISNAD

Modanlı, Mahmut - Özbağ, Fatih. “Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation”. Journal of Mathematical Sciences and Modelling 5/3 (December 1, 2022): 92-98. https://doi.org/10.33187/jmsm.1132139.

JAMA

1.Modanlı M, Özbağ F. Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2022;5:92–98.

MLA

Modanlı, Mahmut, and Fatih Özbağ. “Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation”. Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, Dec. 2022, pp. 92-98, doi:10.33187/jmsm.1132139.

Vancouver

1.Mahmut Modanlı, Fatih Özbağ. Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2022 Dec. 1;5(3):92-8. doi:10.33187/jmsm.1132139

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