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Milstein method for solving fuzzy differential equation | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 11، دوره 18، شماره 3، مرداد و شهریور 2021، صفحه 129-141 اصل مقاله (392.88 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2021.6086 | ||
| نویسندگان | ||
| L. Y. Ji* ؛ C. L. You | ||
| College of Mathematics and Information Science, Hebei University, Baoding 071002, China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Credibility؛ fuzzy differential equation؛ Milstein method؛ semi-implicit Milstein method؛ improved Milstein method؛ mean-stability | ||
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آمار تعداد مشاهده مقاله: 512 تعداد دریافت فایل اصل مقاله: 557 |
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