模糊微分方程边值问题的三类解法

发布时间：2018-06-23 00:22

本文选题：模糊数 + 模糊值函数　；参考：《南京信息工程大学》2017年硕士论文

【摘要】：模糊微分方程是模糊数学的重要组成部分,其求解法在实际中应用广泛.本文主要研究了三种解模糊微分方程边值问题的方法,推广和改进了已有文献的相关结论.全文分为六章,第六章为本文的结论,其余五章内容如下:第一章简述了问题的研究现状与基本方法.第二章列出了本文所需要的预备知识.第三章考虑了线性模糊微分方程边值问题在强广义可微性概念下推广了模糊Laplace变换公式,利用逆变换定理与卷积的性质,提出模糊微分方程边值问题的Laplace变换求解法.第四章以二阶线性模糊微分方程为例,利用模糊微分方程的刻画方程与模糊边值之间的关系,研究了模糊微分方程三角模糊数边值条件下的求解法.第五章考虑了带模糊边值的三阶线性微分方程利用线性变换的性质分离模糊边值,得出了三阶线性微分方程模糊边值问题的一种求解方法.
[Abstract]:Fuzzy differential equation is an important part of fuzzy mathematics, and its solution method is widely used in practice. In this paper, three methods for solving boundary value problems of fuzzy differential equations are studied. This paper is divided into six chapters, the sixth chapter is the conclusion of this paper, the other five chapters are as follows: the first chapter describes the research status and basic methods of the problem. The second chapter lists the preparatory knowledge needed in this paper. In chapter 3, the boundary value problem of linear fuzzy differential equation is considered. The fuzzy Laplace transformation formula is generalized under the concept of strong generalized differentiability. By using the property of inverse transformation theorem and convolution, the Laplace transform method for solving the boundary value problem of fuzzy differential equation is proposed. In the fourth chapter, taking the second order linear fuzzy differential equation as an example, by using the relation between the description equation of fuzzy differential equation and the fuzzy boundary value, we study the solution method under the condition of triangular fuzzy number boundary value of fuzzy differential equation. In chapter 5, we consider the third order linear differential equation with fuzzy boundary value and use the property of linear transformation to separate fuzzy boundary value, and obtain a method to solve the fuzzy boundary value problem of third order linear differential equation.
【学位授予单位】：南京信息工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8

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