aspg-21-3415-1791472412 20261008151332 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Belal Batiha Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan In This paper, we develop the Runge-Kutta numerical method to be applied on neutrosophic problems of high orders, where we present generalized neutrosophic versions of Runge-Kutta methods of rank five, six and seven to use them in finding numerical solutions for some neutrosophic differential problems. In addition, we apply our generalized methods to some solid problems with many illustrated examples and numerical tables for comparing the results and the absolute errors. 2025 593 600 3415 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250346 https://www.americaspg.com/journal/21/article/3415 https://www.americaspg.com/storage/61735270502.pdf