aspg-21-3418-1791475456 20261008160416 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Ahmed Salem Heilat Department of Mathematics, Faculty of Science, Jadara University, P.O. Box 733, Irbid 21110, Jordan In this paper, we study a novel numerical method for finding the neutrosophic numerical solutions to some neutrosophic boundary values problems in differential equations of high orders. The proposed method based on neutrosophic numerical collocations of higher degree polynomials as an approximation to solve the problems. In addition, we provide many mathematical proofs about the existence of the solutions with many different examples and numerical tables that clarify the validity of the proposed method. 2025 18 25 3418 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250403 https://www.americaspg.com/journal/21/article/3418 https://www.americaspg.com/storage/61735271684.pdf