International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3549 2020 2020 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE Iqbal Iqbal Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan Mohammad W. Alomari Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Iqbal H. Jebril Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa 0208, South Africa; Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, 32093, Kuwait Thabet Abdeljawad Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan Nidal Anakira Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, 11942, Jordan Shaher Momani 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 2025 389 398 10.54216/IJNS.250432 https://www.americaspg.com/articleinfo/21/show/3549