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Multi-step gH-difference-based methods for fuzzy differential equations

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Abstract

The main purpose of this paper is to introduce fuzzy Adams–Bashforth (A–B) and fuzzy Adams–Moulton (A–M) methods based on the generalized Hukuhara (gH)-differentiability and employ them as the predictor and corrector, respectively. The local truncation error, stability and convergence of these methods are discussed in the sequel. Finally, some fuzzy linear and nonlinear initial value problems (IVPs) are solved. The numerical results obtained here show that our methods provide a suitable approximation for the exact solution.

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Funding

No funds, grants, or other support were received.

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Author notes

  1. Leila Safikhani, Alireza Vahidi, Tofigh Allahviranloo and Mozhdeh Afshar Kermani have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran

    Leila Safikhani & Tofigh Allahviranloo

  2. Department of Mathematics, College of Science, Yadegar-e-Emam Khomeyni(RAH) Shahr-e-Rey Branch Islamic Azad University, Tehran, Iran

    Alireza Vahidi

  3. Faculty of Engineering and Natural Science, Istinye University, Istanbul, Turkey

    Tofigh Allahviranloo

  4. Department of Mathematics, North Tehran Branch Islamic Azad University, Tehran, Iran

    Mozhdeh Afshar Kermani

Authors
  1. Leila Safikhani
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  2. Alireza Vahidi
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  3. Tofigh Allahviranloo
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  4. Mozhdeh Afshar Kermani
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All authors have contributed to the study’s conception and design.

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Correspondence to Alireza Vahidi.

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Communicated by Marcos Eduardo Valle.

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Safikhani, L., Vahidi, A., Allahviranloo, T. et al. Multi-step gH-difference-based methods for fuzzy differential equations. Comp. Appl. Math. 42, 27 (2023). https://doi.org/10.1007/s40314-022-02167-9

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  • DOI: https://doi.org/10.1007/s40314-022-02167-9

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