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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 25Issue 3PP: 25-36 • 2025

On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System

Raed Hatamleh 1*
1Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan
* Corresponding Author.
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Open Access & Copyright

© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: February 7, 2024 Revised: May 5, 2024 Accepted: September 10, 2024

Abstract

This paper uses finite difference methods to study the numerical solution for neutrosophic Sine-Gordon system in one dimension. We use the explicit method and Crank-Nicholson method. Also, an effective comparison between the results of the two methods has been made, where we obtain the result that Crank-Nicholson method is more accurate than the explicit method, but the explicit method is easier. We also study the stability analysis for each method by using Fourier (Von-Neumann) method and get that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition 𝑟2≤1𝑐2 and 𝑟2≤1.

Keywords

Neutrosophic Sine-Gordon system Crank-Nicholson method Fourier (Von-Neumann) method Nonlinear differential equations

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format_quote
Hatamleh, Raed. "On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, 2025, pp. 25-36. DOI: https://doi.org/10.54216/IJNS.250303
Hatamleh, R. (2025). On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System. International Journal of Neutrosophic Science, Volume 25(Issue 3), 25-36. DOI: https://doi.org/10.54216/IJNS.250303
Hatamleh, Raed. "On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System." International Journal of Neutrosophic Science Volume 25, no. Issue 3 (2025): 25-36. DOI: https://doi.org/10.54216/IJNS.250303
Hatamleh, R. (2025) 'On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System', International Journal of Neutrosophic Science, Volume 25(Issue 3), pp. 25-36. DOI: https://doi.org/10.54216/IJNS.250303
Hatamleh R. On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 3):25-36. DOI: https://doi.org/10.54216/IJNS.250303
R. Hatamleh, "On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, pp. 25-36, 2025. DOI: https://doi.org/10.54216/IJNS.250303
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