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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 27 • Issue 1 • PP: 36-42 • 2026

A Numerical Study of Neutrosophic Finite Difference Method and Some Applications

Isra Al-Shbeil 1*
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,
Ahmad A. Abubaker 2
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,
Sara A. Khalil 3
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,
Maha Alammari 4
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,
Mohamed Soueycatt 5
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,
Abdallah Al-Husban 6
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1Department of Mathematics, faculty of science, University of Jordan, Amman 11942, Jordan
2Faculty of Computer Studies, Arab Open University, Saudi Arabia
3Mathematics Department, Faculty of Science, Applied Science Private University (ASU) Amman, Jordan
4Department of Mathematics, College of Science, King Saud University, Box 22452 Riyadh 11495, Saudi Arabia
5Department of Bioengineering, Al-Andalus Private University for Medical Sciences, Syria
6Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.270104
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: March 01, 2025 Revised: June 04, 2025 Accepted: July 02, 2025
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Abstract

In this paper, we present some results about the neutrosophic-generalized version of finite-difference method, where we prove its essential properties, and we apply it to many different examples to clarify the validity of our work. In addition, some numerical tables related to the results will be clarified and presented.

Keywords

Neutrosophic equation Neutrosophic FDM Numerical table Numerical application

References

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[2]       J. C. Butcher, "Numerical methods for diff. eq.s and applications," The Arabian Journal for Science and Engineering, Dharan, Saudi Arabia, vol. 22, no. 2, pp. 17-29, 1997.

 

[3]       S. H. Lee and J. Kim, "Numerical Solutions for High-Order Differential Equations Using Adaptive Block Methods," Journal of Computational and Applied Mathematics, vol. 387, pp. 112-125, 2021.

 

[4]       A. M. Amin, I. Shah, M. Asif, K. M. Abualnaja, E. E. Mahmoud, and A. Abdel–Aty, "A powerful numerical technique for treating twelfth-order boundary value problems," Open Physics, vol. 18, pp. 1048-1062, 2020.

 

[5]       D. G. Zill, A First Course in Differential Equations With Modeling Application, Brooks/Cole, Cengage Learning, 2008.

 

[6]       P. B. Worland, "Parallel methods for the numerical solutions of ordinary differential equations," IEEE Transactions on Computers, vol. 25, pp. 1045-1048, 1976.

 

[7]       P. C. Chakravarti and P. B. Worland, "A class of self-starting methods for the numerical solution of y f (x, y)," BIT, vol. 11, pp. 368-383, 1971.

 

[8]       R. Al-Deiakeh et al., "Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space," Journal of Ocean Engineering and Science, vol. 7, no. 4, pp. 345-352, 2022.

 

[9]       M. A. Khan and R. S. Gupta, "A Comparative Study of Numerical Techniques for Solving Stiff Differential Equations," Applied Numerical Mathematics, vol. 184, pp. 56-70, 2023.

 

[10]    T. S. Nguyen and P. L. Tran, "Efficient Algorithms for Boundary Value Problems in Differential Equations," Mathematics and Computers in Simulation, vol. 198, pp. 310-325, 2022.

Cite This Article

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format_quote
Al-Shbeil, Isra, Abubaker, Ahmad A., Khalil, Sara A., Alammari, Maha, Soueycatt, Mohamed, Al-Husban, Abdallah. "A Numerical Study of Neutrosophic Finite Difference Method and Some Applications." International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 1, 2026, pp. 36-42. DOI: https://doi.org/10.54216/IJNS.270104
Al-Shbeil, I., Abubaker, A., Khalil, S., Alammari, M., Soueycatt, M., Al-Husban, A. (2026). A Numerical Study of Neutrosophic Finite Difference Method and Some Applications. International Journal of Neutrosophic Science, Volume 27(Issue 1), 36-42. DOI: https://doi.org/10.54216/IJNS.270104
Al-Shbeil, Isra, Abubaker, Ahmad A., Khalil, Sara A., Alammari, Maha, Soueycatt, Mohamed, Al-Husban, Abdallah. "A Numerical Study of Neutrosophic Finite Difference Method and Some Applications." International Journal of Neutrosophic Science Volume 27, no. Issue 1 (2026): 36-42. DOI: https://doi.org/10.54216/IJNS.270104
Al-Shbeil, I., Abubaker, A., Khalil, S., Alammari, M., Soueycatt, M., Al-Husban, A. (2026) 'A Numerical Study of Neutrosophic Finite Difference Method and Some Applications', International Journal of Neutrosophic Science, Volume 27(Issue 1), pp. 36-42. DOI: https://doi.org/10.54216/IJNS.270104
Al-Shbeil I, Abubaker A, Khalil S, Alammari M, Soueycatt M, Al-Husban A. A Numerical Study of Neutrosophic Finite Difference Method and Some Applications. International Journal of Neutrosophic Science. 2026;Volume 27(Issue 1):36-42. DOI: https://doi.org/10.54216/IJNS.270104
I. Al-Shbeil, A. Abubaker, S. Khalil, M. Alammari, M. Soueycatt, A. Al-Husban, "A Numerical Study of Neutrosophic Finite Difference Method and Some Applications," International Journal of Neutrosophic Science, vol. Volume 27, no. Issue 1, pp. 36-42, 2026. DOI: https://doi.org/10.54216/IJNS.270104
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