aspg-21-3239-1791472099 20261008150819 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Raed Hatamleh Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan 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. 2025 25 36 3239 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250303 https://www.americaspg.com/journal/21/article/3239 https://www.americaspg.com/storage/21737027525.pdf