求幂级数和函数的微分方程方法

按照通常求幂级数和函数的思路．对一些幂级数并不能奏效．在某些情况下．可以引入求幂级数和函数的微分方程方法．其主要思路是通过建立和函数的微分方程。将幂级数求和函数问题化为微分方程初值问题来求解．     

Banach空间中非线性脉冲积分微分方程的正解(英)

借助于锥理论，本文讨论Banach空间中非线性脉冲积分微分方程的解．给出一阶脉冲微分方程存在唯一正解的条件及混合型脉冲积分微分方程至少具有两解的条件．     

一类复代数微分方程组解的级

本文利用Zalcman引理研究了一类高阶代数微分方程组解的级的问题，将S．Bank和R．Kaufman，G．Garsegian，以及A．A．Gol’dberg等人的有关代数微分方程的一个结果推广至一类微分方程组中．     

时滞微分方程的不共轭性

本文推广了共轭点和不共轭微分方程的概念，证明了时滞微分方程的不共轭区间不可能是一个单点集．此外，还证明了时滞微分方程的不共轭性与边值问题的可解性之间的联系．     

常微分方程解题模式的构建

为了解决常微分方程教学实践中出现的“断点”问题．在Polya解题观和建构主义学习观的指导下,结合大学常微分方程知识特点,提出基于Polya解题观的常微分方程解题模式。实践表明,本模式对于提高常微分方程教学效果和学生的学习效率具有一定的理论和实践意义．     

多维马尔科夫转制随机微分方程的数值解

由于多维马尔科夫转制随机微分方程不存在解析解,利用Euler—Maruyama方法给出多维马尔科夫转制随机微分方程的渐进数值解,并证明了此数值解收敛到方程的解析解．将单一马尔科夫转制随机微分方程的数值解问题延伸到多维马尔科夫转制情形,增强了马尔科夫转制随机微分方程的适用性．     

二阶非线性微分方程的振动准则

本文给出关于二阶非线性常微分方程和时滞微分方程的一些新的振动准则．     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

非线性中立型延迟微分方程线性Θ-方法的渐近稳定性

1引言近年来,众多学者致力于中立型延迟微分方程算法理论的研究．对线性中立型延迟微分方程数值方法的研究已有众多成果,如文献[2,6-8,11]等．由于存在实质性困难,非线性中立型延迟微分方程数值方法理论研究的文献较少．1997年,Koto在实空间R~d中研究了Natural Runge-Kutta方法关于一类非线性中立型延迟微分方程的渐近稳定性．2000年,Bellen等讨论了连续Runge-Kutta方法关于一类较为特殊的非线性中立型延迟微     

解空间Riesz分数阶扩散方程的一种数值方法

1 引言分数阶微分方程与整数阶(传统)微分方程一样古老[3],它是方程中含有非整数阶导数,在描述各种各样物质的记忆和遗传性质时[4],分数阶导数起着重要的作用．近年来, 分数阶微分方程已广泛应用到众多领域[3],空间分数阶偏微分方程常用于反常扩散模型 [2]．近年来众多学者纷纷研究分数阶微分方程,然而关于分数阶偏微分方程数值方法的研     

一类二阶非线性阻尼微分方程的振动性

研究了一类二阶非线性阻尼微分方程解的振动性,建立了三个新的振动性定理,推广了Cecchi M和Marini M(Rocky Mount J Math,1992,22:1259-1276)的结果.     

关于M/M/1动态排队系统解的半稳定性

本文讨论了两类 M/M/1 动态系统的数学模型 ,利用常微分方程所描述的 M/M/1 系统的结果证明了较复杂的偏微分方程所描述的 M/M/1 系统的一些性质 ,该方法简化了已有结果     

OSCILLATION OF THE SOLUTIONS OF NONLINEAR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.     

THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS

We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.     

On the fractional-order logistic equation

The topic of fractional calculus (derivatives and integrals of arbitrary orders) is enjoying growing interest not only among mathematicians, but also among physicists and engineers (see [E.M. El-Mesiry, A.M.A. El-Sayed, H.A.A. El-Saka, Numerical methods for multi-term fractional (arbitrary) orders differential equations, Appl. Math. Comput. 160 (3) (2005) 683–699; A.M.A. El-Sayed, Fractional differential–difference equations, J. Fract. Calc. 10 (1996) 101–106; A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (2) (1998) 181–186; A.M.A. El-Sayed, F.M. Gaafar, Fractional order differential equations with memory and fractional-order relaxation–oscillation model, (PU.M.A) Pure Math. Appl. 12 (2001); A.M.A. El-Sayed, E.M. El-Mesiry, H.A.A. El-Saka, Numerical solution for multi-term fractional (arbitrary) orders differential equations, Comput. Appl. Math. 23 (1) (2004) 33–54; A.M.A. El-Sayed, F.M. Gaafar, H.H. Hashem, On the maximal and minimal solutions of arbitrary orders nonlinear functional integral and differential equations, Math. Sci. Res. J. 8 (11) (2004) 336–348; R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Wien, 1997, pp. 223–276; D. Matignon, Stability results for fractional differential equations with applications to control processing, in: Computational Engineering in System Application, vol. 2, Lille, France, 1996, p. 963; I. Podlubny, A.M.A. El-Sayed, On Two Definitions of Fractional Calculus, Solvak Academy of science-institute of experimental phys, ISBN: 80-7099-252-2, 1996. UEF-03-96; I. Podlubny, Fractional Differential Equations, Academic Press, 1999] for example). In this work we are concerned with the fractional-order logistic equation. We study here the stability, existence, uniqueness and numerical solution of the fractional-order logistic equation.     

A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS

In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which extends Gaekstatter and Laine＇s result concerning complex differential equations to the systems of algebraic differential equations.     

Cn 中一类复高阶偏微分方程组的允许解

本文研究了多复变中一类复高阶偏微分方程组的允许解的存在性问题,利用多复变值分布理论和技巧,获得一类复高阶偏微分方程组在给定条件下,其允许解的性质.并将单复微分方程组中的一些结果推广到多复变中.     

二阶代数微分方程亚纯解的增长性估计

本文研究了代数微分方程亚纯解的增长级.运用正规族理论,给出了某类二阶代数微分方程亚纯解的增长级的一个估计,该估计依赖于方程的有理函数系数.推广了2001年廖良文与杨重骏的一个结果.     

Adomian decomposition method for solution of differential-algebraic equations

Solutions of differential algebraic equations is considered by Adomian decomposition method. In E. Babolian, M.M. Hosseini [Reducing index and spectral methods for differential-algebraic equations, J. Appl. Math. Comput. 140 (2003) 77] and M.M. Hosseini [An index reduction method for linear Hessenberg systems, J. Appl. Math. Comput., in press], an efficient technique to reduce index of semi-explicit differential algebraic equations has been presented. In this paper, Adomian decomposition method is applied to reduced index problems. The scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed methods.     

Series solutions of coupled differential equations with one regular singular point

We consider two linear second-order ordinary differential equations. r=0 is a regular singular point of these equations. Applying the classical Method of Frobenius, we do not obtain any indicial equation and therefore no solution, because the differential equations are coupled.

In this paper, we present an extended Method of Frobenius on a coupled system of two ordinary differential equations. These equations come from the micropolar theory, which is one of the three kinds of the new 3M physics.