Milstein method for solving fuzzy differential equation
Publish place: Iranian Journal of Fuzzy Systems، Vol: 18، Issue: 3
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-18-3_011
تاریخ نمایه سازی: 30 خرداد 1400
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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