共查询到20条相似文献,搜索用时 240 毫秒
1.
研究了具有广义Hukuhara导数的模糊Logistic方程,将模糊Logistic方程转化成两个常微分方程,分析了模糊Logistic方程平衡点的稳定性.结论表明,模糊Logistic方程平衡点的稳定性不同于确定的Logistic方程,丰富了模糊微分方程研究的内容. 相似文献
2.
在单参数模糊微分方程基础上研究了一阶多参数模糊微分方程和模糊初值问题,利用刻画方程的解与刻画参数的关系给出了多参数模糊微分方程解存在的条件,最后给出了具体算例.表明,多参数模糊微分方程具有广泛的工程应用背景. 相似文献
3.
微分方程模糊初值问题的解 总被引:3,自引:2,他引:1
王磊 《数学的实践与认识》2010,40(5)
研究了一阶线性微分方程模糊初值问题,利用模糊微分方程的刻画方程和初值之间的关系,给出了一阶线性微分方程模糊初值问题的一种求解方法,讨论了同基于Hukuhara微分求解方法之间的关系,证明了在一定条件下两种方法是等价的,文中的实例说明了这一点. 相似文献
4.
《数学的实践与认识》2017,(21)
应用李群理论中的伸缩变换群,把非线性二阶偏微分方程-Burgers方程转化为非线性非齐次一阶常微分方程-Riccati方程,将Riccati方程转化为Bernoulli方程和齐次线性二阶常微分方程,从而找到了Riccati方程的许多解,最后进一步求出了Burgers方程许多新的解析解. 相似文献
5.
Zhou Zhi Yu Zhaoxia 《大学数学》1998,(1)
参考文献[1]利用单调迭代方法研究了模糊微分方程最小解与最大解的存在性,本文在较弱的条件下研究了模糊积分方程的上述问题.本文主要结果的证明比文[1]更简洁. 相似文献
6.
7.
8.
林府标 《数学的实践与认识》2016,(9):241-246
利用李群理论中的伸缩变换群,将二阶非线性偏微分方程-Burgers方程化为一类Riccati方程和三类二阶非线性常微分方程,从而Riccati方程和这三类二阶非线性常微分方程给出了Burgers方程的自相似解的表现形式. 相似文献
9.
本文研究了Fisher方程和Burgers-Fisher方程.运用一种辅助微分方程方法,得到了这两种非线性偏微分方程新的精确行波解. 相似文献
10.
Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法. 相似文献
11.
王磊 《数学的实践与认识》2012,42(10):168-173
研究了n阶线性模糊微分方程的模糊初值问题,将n阶线性模糊微分方程转化成一阶线性模糊微分方程组,利用结构元方法将模糊线性微分方程组转化成两个分明的线性微分方程组,通过分明的线性微分方程组的解构造出原n阶线性模糊微分方程的解.最后,给出了具体的算例. 相似文献
12.
Juan J. Nieto Rosana Rodr��guez-L��pez Manuel Villanueva-Pesqueira 《Fuzzy Optimization and Decision Making》2011,10(4):323-339
Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential
equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order
linear fuzzy differential equation with impulses subject to boundary value conditions. We obtain the explicit solution by
calculating the solutions on each level set and justify that the parametric functions obtained define a proper fuzzy function.
Our results prove that the solution of the fuzzy differential equation of interest is determined, under the appropriate conditions,
by the same Green’s function obtained for the real case. Thus, the results proved extend some theorems given for ordinary
differential equations. 相似文献
13.
M. Oberguggenberger S. Pittschmann 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(3):181-202
This paper is concerned with systems of ordinary differential equations with fuzzy parameters. Applying the Zadeh extension principle to the equations, we introduce the notions of fuzzy solutions and of componentwise fuzzy solutions. The fuzzy extension of the solution operator is shown to provide the unique fuzzy solution as well as the maximal componentwise fuzzy solution. A numerical algorithm based on monotonicity properties of membership functions is presented, together with a proof of convergence. In an interplay of interval analysis and possibility theory, these methods allow to process subjective information on the possible fluctuations of parameters in models involving ordinary differential equations. This is demonstrated in two engineering applications: a queueing model for earthwork and a model of oscillations of bell-towers. 相似文献
14.
Hoang Viet Long Nguyen Thi Kim Son Nguyen Thi My Ha Le Hoang Son 《Fuzzy Optimization and Decision Making》2014,13(4):435-462
Fuzzy hyperbolic partial differential equation, one kind of uncertain differential equations, is a very important field of study not only in theory but also in application. This paper provides a theoretical foundation of numerical solution methods for fuzzy hyperbolic equations by considering sufficient conditions to ensure the existence and uniqueness of fuzzy solution. New weighted metrics are introduced to investigate the solvability for boundary valued problems of fuzzy hyperbolic equations and an extended result for more general classes of hyperbolic equations is initiated. Moreover, the continuity of the Zadeh’s extension principle is used in some illustrative examples with some numerical simulations for \(\alpha \) -cuts of fuzzy solutions. 相似文献
15.
We consider the problem of the resolution of fuzzy equation systems: A certain number of fuzzy inputs and outputs is given. How can we determine a fuzzy relation which describes the behaviour of the object under consideration? When attributing this problem to fuzzy equations in the classical sense it may happen that a solution does not exist. Therefore we introduce fuzzy tolerances as an extension of the solvability conception. For this problem we get the whole solution set by means of posets. Moreover, we consider the inverse problem: How to determine tolerances to get consistency (i.e. at least one solution) for the arising equation system. 相似文献
16.
Yuanguo Zhu 《Fuzzy Optimization and Decision Making》2010,9(2):169-186
Differential equation is a very important field of study not only in theory but in applications, and stochastic differential
equation is also a significant branch of research in theory and applications. Based on the concepts of fuzzy process and fuzzy
differential equation, we present some concepts of stability for fuzzy differential equations. Furthermore we propose the
sufficient and necessary conditions of stability for fuzzy linear differential equations. 相似文献
17.
This paper deals with the solutions of fuzzy Volterra integral equations with separable kernel by using fuzzy differential transform method (FDTM). If the equation considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. To this end, we have obtained several new results to solve mentioned problem when FDTM has been applied. In order to show this capability and robustness, some fuzzy Volterra integral equations are solved in detail as numerical examples. 相似文献
18.
Rosana Rodríguez-Lpez 《Fuzzy Sets and Systems》2008,159(11):1384-1409
The peculiarity of the Hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations. In this work, we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method. Fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic ‘linear’ differential problems is also provided. 相似文献
19.
《Fuzzy Sets and Systems》1987,23(2):271-279
A method for the solution of multivariable fuzzy equations and inequalities is proposed. The proposed method is an extension of Sanchez' technique for a single fuzzy equation. A numerical example is given. 相似文献
20.
本文从探讨与函数密切相关的定性函数入手,研究了微分方程组解的有界性质,并由此给出某些高阶及2阶非线性微分方程解的有界性的一些结论,它们包合并推广了[3~8]的有关结果 相似文献