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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 4 , PP: 389-398, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems

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

  • 1 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE - (i.batiha@zuj.edu.jo)
  • 2 Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan - (mwomath@gmail.com)
  • 3 Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan - (i.jebril@zuj.edu.jo)
  • 4 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 - (tabdeljawad@psu.edu.sa)
  • 5 Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan - (nanakira@su.edu.om)
  • 6 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, 11942, Jordan - (s.momani@ju.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.250432

    Received: November 26, 2024 Revised: December 24, 2024 Accepted: January 26, 2024
    Abstract

    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.

    Keywords :

    Obreschkoff formula , Boundary value problems , Shooting method , Approximations

    References

    [1] M. W. Alomari, I. M. Batiha, N. Anakira, I. H. Jebril, S. Momani, Euler-Maclaurin method for approximating solutions of initial value problems, International Journal of Robotics and Control Systems, vol. 5, no. 1, pp. 366-380, 2025.

    [2] M. Islam, ”A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods,” American Journal of Computational Mathematics, vol. 5, no. 3, pp. 393-404, 2020.

    [3] R. L. Burden, J. D. Faires, Numerical Analysis, Brooks/Cole, Boston, 2011.

    [4] W. Alshanti, A. Alshanty, and R. Khalil, Atomic solution for both ordinary and fractional abstract Cauchy problem in tensor product form, Gulf Journal of Mathematics, vol. 18, no. 1, pp. 189-196, 2024.

    [5] Berredjem, N., Maayah, B., Abu Arqub, O. (2022). A numerical method for solving conformable fractional integrodifferential systems of second-order, two-points periodic boundary conditions. Alexandria Engineering Journal, 61(7), 5699-5711.

    [6] M. Benchohra, S. Hamani, and A. Ouahab, ’Applying periodic and anti-periodic boundary conditions in fractional differential equations,’ Boundary Value Problems, vol. 2023, no. 1, pp. 1-15, 2023.

    [7] A. A. Al-Nana, I. M. Batiha, S. Momani, A numerical approach for dealing with fractional boundary value problems, Mathematics, vol. 11, no. 19, pp. 4082, 2023.

    [8] A. Atangana, D. Baleanu, ”Fractional calculus with an integral boundary condition for solving anomalous diffusion equations,” Chaos, Solitons Fractals, vol. 134, pp. 109694, 2020.

    [9] M.W. Alomari, I. M. Batiha, S. Momani, New higher-order implicit method for approximating solutions of the initial value problems, Journal of Applied Mathematics and Computing, vol. 64, no. 1-2, pp. 1-15, 2024.

    Cite This Article As :
    M., Iqbal. , W., Mohammad. , H., Iqbal. , Abdeljawad, Thabet. , Anakira, Nidal. , Momani, Shaher. New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 389-398. DOI: https://doi.org/10.54216/IJNS.250432
    M., I. W., M. H., I. Abdeljawad, T. Anakira, N. Momani, S. (2025). New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science, (), 389-398. DOI: https://doi.org/10.54216/IJNS.250432
    M., Iqbal. W., Mohammad. H., Iqbal. Abdeljawad, Thabet. Anakira, Nidal. Momani, Shaher. New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science , no. (2025): 389-398. DOI: https://doi.org/10.54216/IJNS.250432
    M., I. , W., M. , H., I. , Abdeljawad, T. , Anakira, N. , Momani, S. (2025) . New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science , () , 389-398 . DOI: https://doi.org/10.54216/IJNS.250432
    M. I. , W. M. , H. I. , Abdeljawad T. , Anakira N. , Momani S. [2025]. New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science. (): 389-398. DOI: https://doi.org/10.54216/IJNS.250432
    M., I. W., M. H., I. Abdeljawad, T. Anakira, N. Momani, S. "New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems," International Journal of Neutrosophic Science, vol. , no. , pp. 389-398, 2025. DOI: https://doi.org/10.54216/IJNS.250432

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