ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 25Issue 4PP: 10-17 • 2025

The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems

Belal Batiha 1*
1Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan
* Corresponding Author.
Received: Jun 08, 2024 Revised: September 02, 2024 Accepted: December 22, 2024

Abstract

In this paper, we present a numerical approach to the seventh rank refined neutrosophic Runge-Kutta numerical method, where we provide the theoretical basis of this formula to be applicable on refined neutrosophic differential equations. In addition, we provide numerical tables to compare the validity of this new method with other methods, as well as a clear computation of absolute errors in terms of refined neutrosophic numbers.

Keywords

Refined neutrosophic number Refined neutrosophic Runge-Kutta of rank seven Numerical error absolute error

References

[1] J. C. Butcher and M. T. Diamantakis, "DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods," Numeric. Algorithm, vol. 17, pp. 121–145, 1998.

 

[2] J. C. Butcher, "Numerical methods for differential equations and applications," Arabian J. Sci. Eng., vol. 22, no. 2, pp. 17–29, 1997.

 

[3] J. R. Cash, "Block Runge-Kutta methods for numerical integration of initial value problems in ordinary differential equations Part II: The stiff case," Math. Comput, vol. 40, no. 161, pp. 193–206, 1983.

 

[4] J. Wang, Y. Luo, and X. Li, "A class of efficient implicit Runge-Kutta methods for stiff ordinary differential equations," J. Comput. Appl. Math., vol. 401, art. No. 113794, 2022. DOI: 10.1016/j.cam.2021.113794.

[5] J. R. Cash, "Runge-Kutta methods for the solution of stiff two-point boundary value problems," Appl. Numer. Math., vol. 22, pp. 165–177, 1996.

 

[6] F. Smarandache, Introduction to Neutrosophic Statistics, Sitech & Education Publishing, USA, 2014.

 

[7] D. A. Voss and M. J. Casper, "Efficient split linear multistep methods for stiff ordinary differential equations," SIAM J. Sci. Stat. Comput., vol. 19, no. 5, pp. 990–999, 1989.

 

[8] D. A. Voss, "Factored two-step Runge-Kutta methods," Appl. Math. Compute, vol. 31, pp. 361–368, 1989.

 

[9] D. A. Voss, "Fifth-order exponentially fitted formula," SIAM J. Numer. Anal., vol. 25, no. 3, pp. 670–678, 1988.

 

[10] A. A. Abubaker, M. Abualhomos, K. Matarneh, and A. Al-Husban, "A numerical approach for the algebra of two-fold," Neutrosophic Sets Syst., vol. 75, pp. 181–195, 2025.

 

[11] M. A. Khoshnam, S. A. Kheirandish, and H. R. Naderi, "Numerical Methods for Neutrosophic Boundary Value Problems: Applications and Solutions," International Journal of Neutrosophic Science, vol. 24, no. 3, pp. 150–162, 2023. DOI: 10.54216/IJNS.240301.

[12] S. M. and A. N. Mera, "Fuzzy logic used to solve ODEs of second order under neutrosophic initial conditions," Int. J. Neutrosophic Sci., vol. 23, no. 1, pp. 51–58, 2024. DOI: 10.54216/IJNS.230104.

 

[13] S. Topal, F. Tas, S. Broumi, and O. Ayhan, "Applications of neutrosophic logic of smart agriculture via Internet of Things," Int. J. Neutrosophic Sci., vol. 12, no. 2, pp. 105–115, 2020. DOI: 10.54216/IJNS.120205.

 

[14] A. Shihadeh, K. A. M. Matarneh, R. Hatamleh, R. B. Y. Hijazeen, M. O. Al-Qadri, and A. Al-Husban, "An example of two-fold fuzzy algebras based on neutrosophic real numbers," Neutrosophic Sets Syst., vol. 67, pp. 169–178, 2024.

 

[15] A. F. Salamah and R. M. Dallah, "A study of neutrosophic Bernoulli and Riccati equations using the one-dimensional geometric AH-Isometry," J. Neutrosophic Fuzzy Syst., vol. 5, no. 1, pp. 30–40, 2023. DOI: 10.54216/JNFS.050104.

 

[16] T. Hamadneh, A. Abbes, I. A. Falahah, Y. A. Al-Khassawneh, A. S. Heilat, A. Al-Husban, and A. Ouannas, "Complexity and chaos analysis for two-dimensional discrete-time predator-prey Leslie-Gower model with fractional orders," Axioms, vol. 12, no. 6, art. no. 561, 2023.

 

[17] M. Sahin and N. Olgun, “On the Refined AH-Isometry and Its Applications in Refined Neutrosophic Surfaces,” Galoitica: Journal of Mathematical Structures and Applications, vol. 2, no. 1, pp. 21–28, 2022.

 

[18] F. Al-Sharqi, “Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields,” Journal of Neutrosophic and Fuzzy Systems, vol. 5, no. 2, pp. 45–58, 2023.

 

[19] A. M. Al-Odhari, “Some Algebraic Structure of Neutrosophic Matrices,” Journal of Algebraic Structures and Their Applications, vol. 10, no. 3, pp. 158–167, 2023.

 

[20] B. Batiha, "New solution of the Sine-Gordon equation by the Daftardar-Gejji and Jafari Method," Symmetry, vol. 14, no. 1, art. No. 57, 2022.

 

[21] B. Batiha, G. F. Alayed, O. Hatamleh, A. S. Heilat, H. Zureigat, and O. Bazighifan, "Solving multispecies Lotka-Volterra equations by the Daftardar-Gejji and Jafari Method," Int. J. Math. Math. Sci., vol. 2022, art. No. 1839796.

 

[22] O. Ala’yed, B. Batiha, R. Abdelrahim, and A. Jawarneh, "On the numerical solution of the nonlinear Bratu type equation via quintic B-spline method," J. Interdiscip. Math., vol. 22, no. 4, pp. 405–413, 2019.

 

[23] M. Abualhomos, W. M. M. Salameh, M. Bataineh, M. O. Al-Qadri, A. Alahmade, and A. Al-Husban, "An effective algorithm for solving weak fuzzy complex Diophantine equations in two variables," Int. J. Neutrosophic Sci., vol. 23, no. 4, pp. 386–394, 2024.

 

[24] A. Al-Husban, R. C. Karoun, A. S. Heilat, M. Al Horani, A. A. Khennaoui, G. Grassi, and A. Ouannas, "Chaos in a two-dimensional fractional discrete Hopfield neural network and its control," Alexandria Eng. J., vol. 75, pp. 627–638, 2023.

 

[25] A. S. Heilat, R. C. Karoun, A. Al-Husban, A. Abbes, M. Al Horani, G. Grassi, and A. Ouannas, "The new fractional discrete neural network model under electromagnetic radiation: Chaos, control and synchronization," Alexandria Eng. J., vol. 76, pp. 391–409, 2023.

Cite This Article

Choose your preferred format

format_quote
Batiha, Belal. "The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, 2025, pp. 10-17. DOI: https://doi.org/10.54216/IJNS.250402
Batiha, B. (2025). The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems. International Journal of Neutrosophic Science, Volume 25(Issue 4), 10-17. DOI: https://doi.org/10.54216/IJNS.250402
Batiha, Belal. "The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems." International Journal of Neutrosophic Science Volume 25, no. Issue 4 (2025): 10-17. DOI: https://doi.org/10.54216/IJNS.250402
Batiha, B. (2025) 'The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems', International Journal of Neutrosophic Science, Volume 25(Issue 4), pp. 10-17. DOI: https://doi.org/10.54216/IJNS.250402
Batiha B. The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 4):10-17. DOI: https://doi.org/10.54216/IJNS.250402
B. Batiha, "The Runge-Kutta Numerical Method of Rank Seven for the Solutions of Some Refined Neutrosophic Differential Problems," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, pp. 10-17, 2025. DOI: https://doi.org/10.54216/IJNS.250402
Digital Archive Ready