International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3889 2020 2020 Faculty of Computer Studies, Arab Open University, Saudi Arabia Abdallah Abdallah Applied Science Private University Amman, 11931, Jordan Mayada Abualhomos The university of Jordan, Aqaba Department of computer information systems, Jordan Ahmed Atallah Alsaraireh 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 Abdallah Al Al-Husban 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 2025 01 08 10.54216/IJNS.260401 https://www.americaspg.com/articleinfo/21/show/3889