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

Iqbal M.; Mohammad W.; Iqbal H.; Thabet; Nidal; Shaher

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

Full Length Article

Volume 25 • Issue 4 • PP: 389-398 • 2025

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

Iqbal M. Batiha ^1*

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,

Mohammad W. Alomari ²

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,

Iqbal H. Jebril ³

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,

Thabet Abdeljawad ⁴

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,

Nidal Anakira ⁵

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,

Shaher Momani ⁶

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¹Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE

²Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan

³Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan

⁴Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Tech

⁵Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan

⁶Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE; Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.250432

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

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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

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Batiha, Iqbal M., Alomari, Mohammad W., Jebril, Iqbal H., Abdeljawad, Thabet, Anakira, Nidal, Momani, Shaher. "New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, 2025, pp. 389-398. DOI: https://doi.org/10.54216/IJNS.250432

Batiha, I., Alomari, M., Jebril, 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, Volume 25(Issue 4), 389-398. DOI: https://doi.org/10.54216/IJNS.250432

Batiha, Iqbal M., Alomari, Mohammad W., Jebril, Iqbal H., Abdeljawad, Thabet, Anakira, Nidal, Momani, Shaher. "New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems." International Journal of Neutrosophic Science Volume 25, no. Issue 4 (2025): 389-398. DOI: https://doi.org/10.54216/IJNS.250432

Batiha, I., Alomari, M., Jebril, 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, Volume 25(Issue 4), pp. 389-398. DOI: https://doi.org/10.54216/IJNS.250432

Batiha I, Alomari M, Jebril I, Abdeljawad T, Anakira N, Momani S. New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 4):389-398. DOI: https://doi.org/10.54216/IJNS.250432

I. Batiha, M. Alomari, I. Jebril, T. Abdeljawad, N. Anakira, S. Momani, "New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, pp. 389-398, 2025. DOI: https://doi.org/10.54216/IJNS.250432

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