(2002-5686)求解模糊微分方程的Milstein方法

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-01-27 DOI:10.22111/IJFS.2021.5946

L. Ji, C. L. You

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引用次数: 0

摘要

为了求解由Liu过程驱动的模糊微分方程，本文提出了三种Milstein格式:显式Milstein格式、半隐式Milstein格式和改进Milstein格式。利用半隐式方法修正误差，构造了改进的Milstein格式，其误差为模糊微分方程的精确解与Milstein格式的解之间的差值。证明了这些数值方法具有很强的二阶收敛性。在此基础上，提出并分析了模糊微分方程数值格式的平均稳定性概念。对于一个线性检验方程，证明了改进Milstein格式的平均稳定区域大于显式Milstein格式。最后，通过数值算例验证了这些格式的准确性和有效性。

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(2002-5686) Milstein method for solving fuzzy differential equation

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 analysed. 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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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.