基于随机算法求解模糊微分方程的预测-校正法的数值精度

IF 1.3 Q2 MATHEMATICS, APPLIED
M. A. Fariborzi Araghi, Hasan Barzegar Kelishami
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引用次数: 2

摘要

在广义h -可微性条件下,提出了一种基于预测校正方法(pc -方法)求解模糊微分方程的可靠方案。为此,采用随机算法(SA)和CESTAC*方法对结果进行验证。证明了该方法的数值精度,并在此基础上给出了一种算法。为了实现c++代码,使用了CADNA†库。在这种情况下,找到最优节点数和最优步长。这些示例说明了使用SA代替浮点算术(FPA)的效率和重要性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical Accuracy of the Predictor-Corrector Method to Solve Fuzzy Differential Equations Based on the Stochastic Arithmetic
In this work, a reliable scheme is proposed to solve fuzzy differential equation based on the predictor-corrector methods (PC-methods) under generalized H-differentiability. For this purpose, the stochastic arithmetic(SA) and the CESTAC* method are applied to validate the results. Also, the numerical accuracy of the method is proved and an algorithm is given based on the new arithmetic. In order to implement C++ codes, the CADNA† library is used. In this case, the optimal number of nodes and optimal step size are found. The examples illustrate the efficiency and importance of using the SA in place of the floating-point arithmetic(FPA).
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
13
审稿时长
40 weeks
期刊介绍: Fuzzy Information and Engineering—An International Journal wants to provide a unified communication platform for researchers in a wide area of topics from pure and applied mathematics, computer science, engineering, and other related fields. While also accepting fundamental work, the journal focuses on applications. Research papers, short communications, and reviews are welcome. Technical topics within the scope include: (1) Fuzzy Information a. Fuzzy information theory and information systems b. Fuzzy clustering and classification c. Fuzzy information processing d. Hardware and software co-design e. Fuzzy computer f. Fuzzy database and data mining g. Fuzzy image processing and pattern recognition h. Fuzzy information granulation i. Knowledge acquisition and representation in fuzzy information (2) Fuzzy Sets and Systems a. Fuzzy sets b. Fuzzy analysis c. Fuzzy topology and fuzzy mapping d. Fuzzy equation e. Fuzzy programming and optimal f. Fuzzy probability and statistic g. Fuzzy logic and algebra h. General systems i. Fuzzy socioeconomic system j. Fuzzy decision support system k. Fuzzy expert system (3) Soft Computing a. Soft computing theory and foundation b. Nerve cell algorithms c. Genetic algorithms d. Fuzzy approximation algorithms e. Computing with words and Quantum computation (4) Fuzzy Engineering a. Fuzzy control b. Fuzzy system engineering c. Fuzzy knowledge engineering d. Fuzzy management engineering e. Fuzzy design f. Fuzzy industrial engineering g. Fuzzy system modeling (5) Fuzzy Operations Research [...] (6) Artificial Intelligence [...] (7) Others [...]
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