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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 3 , PP: 76-91, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem

Iqbal M. Batiha 1 * , Mohammad W. Alomari 2 , Nidal Anakira 3 , Saad Meqdad 4 , Iqbal H. Jebril 5 * , Shaher Momani 6

  • 1 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan - (i.batiha@zuj.edu.jo)
  • 2 Department of Mathematics, Jadara University, P.O. Box 733, Irbid, P.C. 21110, Jordan - (mwomath@gmail.com)
  • 3 Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Jadara Research Center, Jadara University, Irbid 21110, Jordan - (nanakira@su.edu.om)
  • 4 Applied science private university, Amman 11937, Jordan - (s meqdad@asu.edu.jo)
  • 5 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan - (i.jebril@zuj.edu.jo)
  • 6 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, Jordan - (s.momani@ju.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.250308

    Received: February 13, 2024 Revised: May 14, 2024 Accepted: September 18, 2024
    Abstract

    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.

    Keywords :

    Euler-Maclaurin formula , Runge-Kutta method , ODE , Darboux&rsquo , s formula , Approximations

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    Cite This Article As :
    M., Iqbal. , W., Mohammad. , Anakira, Nidal. , Meqdad, Saad. , H., Iqbal. , Momani, Shaher. Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 76-91. DOI: https://doi.org/10.54216/IJNS.250308
    M., I. W., M. Anakira, N. Meqdad, S. H., I. Momani, S. (2025). Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem. International Journal of Neutrosophic Science, (), 76-91. DOI: https://doi.org/10.54216/IJNS.250308
    M., Iqbal. W., Mohammad. Anakira, Nidal. Meqdad, Saad. H., Iqbal. Momani, Shaher. Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem. International Journal of Neutrosophic Science , no. (2025): 76-91. DOI: https://doi.org/10.54216/IJNS.250308
    M., I. , W., M. , Anakira, N. , Meqdad, S. , H., I. , Momani, S. (2025) . Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem. International Journal of Neutrosophic Science , () , 76-91 . DOI: https://doi.org/10.54216/IJNS.250308
    M. I. , W. M. , Anakira N. , Meqdad S. , H. I. , Momani S. [2025]. Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem. International Journal of Neutrosophic Science. (): 76-91. DOI: https://doi.org/10.54216/IJNS.250308
    M., I. W., M. Anakira, N. Meqdad, S. H., I. Momani, S. "Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem," International Journal of Neutrosophic Science, vol. , no. , pp. 76-91, 2025. DOI: https://doi.org/10.54216/IJNS.250308

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