International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3239 2020 2020 Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Raed Raed 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 2025 25 36 10.54216/IJNS.250303 https://www.americaspg.com/articleinfo/21/show/3239