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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 2

Numerical Solution of Fuzzy Differential Equations by two-step Modified Simpson Rule

Ekhtiar Khodadadi(Islamic Azat University)0000-0002-6679-4873
Mesut Karabacak(ATATURK UNIVERSITY)0000-0002-0057-8115
Ercan Celık(Kyrgyz-Turkish Manas University)0000-0001-5971-7653
Pages
—
Publication Date
2026-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The convergence and stability of the proposed rule are demonstrated, and its application is shown with some examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For the fuzzy first-order initial value issue, a numerical explicit two-step modified Simpson rule is presented in this study.
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Key Findings & Data:For the fuzzy first-order initial value issue, a numerical explicit two-step modified Simpson rule is presented in this study.
💡
Conclusion & Impact:The convergence and stability of the proposed rule are demonstrated, and its application is shown with some examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy differential equations · fuzzy Cauchy problem · two-step methods

Abstract

For the fuzzy first-order initial value issue, a numerical explicit two-step modified Simpson rule is presented in this study. The convergence and stability of the proposed rule are demonstrated, and its application is shown with some examples.

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Cite This Article

Khodadadi, E., Karabacak, M., Celık, E. (2026). Numerical Solution of Fuzzy Differential Equations by two-step Modified Simpson Rule. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 2. https://doi.org/10.47000/tjmcs.1721161

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References (18)

  1. Allahviranloo, T., Ahmady, N., Ahmady, E., Numerical solution of fuzzy differential equations by predictor-corrector method, Information Sciences, 177(2007), 1633–1647.
  2. Chang, S.S.L., Zadeh, L.A., On fuzzy mapping and control, IEEE Transactions on Systems Man Cybernetics, 2(1972), 330–334.
  3. Dubois, D., Prade, H., Operations on fuzzy numbers, International Journal of Systems Science, 9(1978), 613–626.
  4. Friedman, M., Ma, M., Kandel, A., Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106(1999), 35–48.
  5. Ivaz, K., Khastan, A., Nieto, J.J., A numerical method for fuzzy differential equations and hybrid fuzzy differential equations, Hindawi Publishing Corporation Abstract and Applied Analysis, 10(2013).
  6. Kaleva O. Fuzzy differential equations, Fuzzy Sets and Systems, 24(1987), 301–317.
  7. Kaleva O. Interpolation of fuzzy data. Fuzzy Set and System, 60(1994), 63–70,
  8. Kaleva O. The Cauchy problem for fuzzy differential equations, Fuzzy sets and System, 35(1990).
  9. Kanagarajan, K., Muthukumar, S., Indrakumar S., Modified two-step Simpson method for solving the fuzzy differential equations and the dependency problem, IOSR Journal of Mathematics, 10(2014), 19–26.
  10. Kandel, A., Byatt, W.J., Fuzzy sets, Fuzzy algebra, and fuzzy statistics, Proceedings of the IEEE, 66(1978), 1619–1639.
  11. Kandel, W., Byatt, W.J., Fuzzy differential equations, in Proceedings of the International Conference on Cybernetics and Society, (1978), 1213–1216, IEEE, Tokyo, Japan.
  12. Khastan, A., Bahrami, F., Ivaz, K., New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability, Boundary Value Problems 2009.
  13. Khastan, A., Ivaz, K., Numerical solution of fuzzy differential equations by Nystrom method, Chaos, Solitons & Fractals, 41(2009) 859–868.
  14. Khodadadi, E., C¸ elik, E., The variational iteration method for fuzzy fractional differential equations with uncertainty, Fixed Point Theorems nd Their Applications, 2013, 1–13.
  15. Khodadadi, E., Karabacak, M., C¸ elik, E., Numerical solutions of fuzzy linear fractional differential equations with Laplace transforms under Caputo-type H-differentiability, Journal of Mathematics, 15(2025).
  16. Ma, M., Friedman, M., Kandel, A., Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems, 105(1999), 133–138.
  17. Nieto, J.J., Khastan, A., Ivaz, K., Numerical solution of fuzzy differential equations under generalized differentiability, Nonlinear Analysis: Hybrid Systems, 3(2009), 700–707.
  18. Sindu, S.D., Ganesan, K., Numerical solution of first order fuzzy differential equations by Simpson’s rule. British Journal of Mathematics & Computer Science, 18(2016), 1–13.