Volume 25 • Issue 4 • PP: 240-249 • 2025
Applying Block Method for the Numerical Solutions of the Second Order n-Refined Neutrosophic ODE for n=2, 3
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Abstract
In this paper, we study the applications of block method to find the numerical solutions of some neutrosophic differential problems, where we discuss the approximated n-refined neutrosophic solutions and absolute n-refined neutrosophic errors in two special cases for n=2, and n=3. In addition, we list the numerical tables of our results.
Keywords
References
[1] J. B. Rosser, Runge-Kutta for all seasons, in SIAM Rev. 9, 417-452 (1967).
[2] L. F. Shampine and H. F. Watts, Block implicit one-step method, in Math. Comp, 23, 731-740(1969).
[3] P. B. Worland, Parallel methods for the numerical solutions of ordinary differential equations, in IEEE Transactions on Computers, 25, 1045-1048 (1976).
[4] Z. A. Majid, M. B. Suleiman, F. Ismail and M. Othman, 2-point implicit block one-step method half Gauss-Seidel for solving first order ordinary differential equations, in Matematika, Jabatan UTM, 19, 91-100 (2003).
[5] P. C. Chakravarti and P. B. Worland, A class of self-starting methods for the numerical solution of y f (x, y), in BIT, 11, 368-383 (1971).
[6] Shihadeh, A., Matarneh, K. A. M., Hatamleh, R., Al-Qadri, M. O., & Al-Husban, A. (2024). On The Two-Fold Fuzzy n-Refined Neutrosophic Rings For 2≤ 3. Neutrosophic Sets and Systems, 68, 8-25.
[7] Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Randa Bashir Yousef Hijazeen, Mowafaq Omar Al-Qadri, Abdallah Al-Husban.(2024). An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers, Neutrosophic Sets and Systems, 67,169-178.
[8] S. H. Karim, A. S. Jain, and R. Y. Choudhary, "Properties of neutrosophic ideals in semigroups and their applications," Journal of Mathematical Structures, vol. 48, no. 4, pp. 217-230, 2022.
[9] S. M. R. S. V. Sarma, R. Kumar, and P. V. S. R. K. Kumar, "Complex cubic intuitionistic fuzzy sets and their applications to semigroups and ring theory," Mathematical Logic Quarterly, vol. 64, no. 2, pp. 150-160, 2024.
[10] F. Smarandache, "Neutrosophic singular boundary value problems and their applications," Neutrosophic Sets and Systems, vol. 35, pp. 108-115, 2023.
[11] J. Zhang and Q. Yang, "The k-threshold conversion number for graph products and its generalizations in neutrosophic logic," Mathematical Logic Quarterly, vol. 61, no. 6, pp. 612-627, 2023.
[12] Raed Hatamleh, Abdallah Al-Husban, K. Sundareswari, G.Balaj, M.Palanikumar (2025). Complex Tangent Trigonometric Approach Applied to (γ, τ)-Rung Fuzzy Set using Weighted Averaging, Geometric Operators and its Extension. Communications on Applied Nonlinear Analysis, 32 (5), PP: 133-144.
[13] M. G. Ali, S. M. Amin, and H. R. Ghaffari, "Generalized weighted operators and their applications in fuzzy decision-making systems based on trigonometric functions," Journal of Applied Mathematics and Computational Mechanics, vol. 20, no. 4, pp. 113-127, 2024.
[14] A. M. Peralta and D. Cabezas, "Linear orthogonality preservers between function spaces associated with commutative JB*-triples," J. Math. Phys., vol. 63, no. 5, p. 053501, 2022, doi: 10.1063/5.0083580.
[15] Zolotarev, V. A., & Koudelka, L. (2021). The behavior of fuzzy systems under uncertainty in environmental modeling. Journal of Computational and Applied Mathematics, 381, 112874.
[16] E. G. Belyaev and A. I. Lisin, "Commutative and Noncommutative Operator Models in Quantum Information Theory," J. Math. Phys., vol. 62, no. 7, p. 073502, 2021, doi: 10.1063/5.0052819.
[17] M. L. Liao, Z. S. Zhou, and Z. X. Liu, "A new approach for solving fuzzy Diophantine equations with applications to cryptography," Fuzzy Optimization and Decision Making, vol. 22, no. 3, pp. 293-307, 2023.
[18] X. Liu, H. Li, and H. Zhang, "A hybrid cryptographic protocol based on fuzzy logic and split-complex numbers," Journal of Mathematical Cryptography, vol. 27, pp. 45-60, 2024.
[19] T. A. Doe, P. R. Singh, and L. V. Gupta, "Study of neutrosophic ideals in ternary semigroups and their algebraic properties," Journal of Algebraic Structures and Applications, vol. 42, no. 3, pp. 155-170, 2024..
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.