aspg-21-3549-1791475361 20261008160241 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Iqbal M. Batiha Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE Mohammad W. Alomari Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan Iqbal H. Jebril Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Thabet Abdeljawad Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Tech Nidal Anakira Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan Shaher Momani Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, 11942, Jordan This paper is devoted to introducing a novel numerical approach for approximating solutions to Boundary Value Problems (BVPs). Such an approach will be carried out by using a new version of the shooting method, which would convert the BVP into a linear system of two initial value problems. This system can then be solved by the so-called Obreschkoff approach. The numerical solution of the main BVP will ultimately be a linear combination of the solutions of the two system of equations. Two physical applications will be presented in order to confirm that the suggested numerical technique is valid. 2025 389 398 3549 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250432 https://www.americaspg.com/journal/21/article/3549 https://www.americaspg.com/storage/21738506257.pdf