aspg-21-3889-1792501863 20261020131103 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 4 Ahmad A. Abubaker Faculty of Computer Studies, Arab Open University, Saudi Arabia Mayada Abualhomos Applied Science Private University Amman, 11931, Jordan Ahmed Atallah Alsaraireh The university of Jordan, Aqaba Department of computer information systems, Jordan Abdallah Al-Husban Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan This paper is dedicated to study for the first time the applications of neutrosophic BDF and CDF Newton's methods for finding the numerical solutions of some different problems related to the derivations from first and second order applied on neutrosophic-tabulated functions, where we apply those novel methods on some problems and list the solutions by using the numerical tables. In addition, we provide a theoretical discussion and description of these methods to be applicable on other numerical problems. 2025 01 08 3889 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260401 https://www.americaspg.com/journal/21/article/3889 https://www.americaspg.com/storage/31749743933.pdf