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Cites:

Information Journal Paper

Title

Milstein method for solving fuzzy differential equation

Pages

  129-141

Abstract

 To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.

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    APA: Copy

    Ji, L.Y., & You, C.L.. (2021). Milstein method for solving fuzzy differential equation. IRANIAN JOURNAL OF FUZZY SYSTEMS, 18(3 ), 129-141. SID. https://sid.ir/paper/413133/en

    Vancouver: Copy

    Ji L.Y., You C.L.. Milstein method for solving fuzzy differential equation. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2021;18(3 ):129-141. Available from: https://sid.ir/paper/413133/en

    IEEE: Copy

    L.Y. Ji, and C.L. You, “Milstein method for solving fuzzy differential equation,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 18, no. 3 , pp. 129–141, 2021, [Online]. Available: https://sid.ir/paper/413133/en

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