International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3244 2020 2020 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Iqbal Iqbal Department of Mathematics, Jadara University, P.O. Box 733, Irbid, P.C. 21110, Jordan Mohammad W. Alomari Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Jadara Research Center, Jadara University, Irbid 21110, Jordan Nidal Anakira Applied science private university, Amman 11937, Jordan Saad Meqdad Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Iqbal H. Jebril Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, Jordan Shaher Momani This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems. 2025 2025 76 91 10.54216/IJNS.250308 https://www.americaspg.com/articleinfo/21/show/3244