共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient. 相似文献
2.
In his paper the notions of two-point Padé-type and two-point Padé approximants are generalized for multivariate functions, with a generating denominator polynomial of general form. The multivariate two-point Padé approximant can be expressed as a ratio of two determinants and computed recursively using the E-algorithm. A comparison is made with previous definitions by other authors using particular generating denominator polynomials. The last section contains some convergence results. 相似文献
3.
Zhuang Rongkun 《Annals of Differential Equations》2006,22(2):234-240
In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical Sturm comparison theorems. 相似文献
4.
In this paper we present some known results on cumulative measures of information, study their properties and relate these definitions to concepts of reliability theory. We give some relations of these measures of discrimination with some well-known stochastic orders and with the relative reversed hazard rate order. We investigate also a stochastic comparison among the empirical cumulative measures that can be related to the cumulative measures. Large part of this paper is a survey article; however, in the last section, we define a new measure of discrimination between residual lifetimes and study some of its properties. 相似文献
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6.
通过建立几个微分不等式将经典的微分方程零点比较定理推广到二阶非线性微分方程,得到若干新的结论. 相似文献
7.
Jia-wei Dou Kai-tai Li 《应用数学学报(英文版)》2006,22(2):211-218
In this paper,for a semi-linear parabolic partial differential equations with impulsive effects,theexistence-comparison theorem and comparison principles are established using the method of upper and lowersolutions.These results are applied to obtain the stability results of the steady-state solutions in a reaction-diffusion equations modelling two competing species with instantaneous stocking. 相似文献
8.
The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type of characterization for the fractional powers of second order partial differential operators in some class. We also get a Poisson formula and a system of Cauchy–Riemann equations for the extension. The method is applied to the fractional harmonic oscillator H σ = (? Δ + |x|2)σ to deduce a Harnack's inequality. A pointwise formula for H σ f(x) and some maximum and comparison principles are derived. 相似文献
9.
S.L. Campbell W. Marszalek 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(1):18-42
The idea of the index of a differential algebraic equation (DAE) (or implicit differential equation) has played a fundamental role in both the analysis of DAEs and the development of numerical algorithms for DAEs. DAEs frequently arise as partial discretizations of partial differential equations (PDEs). In order to relate properties of the PDE to those of the resulting DAE it is necessary to have a concept of the index of a possibly constrained PDE. Using the finite dimensional theory as motivation, this paper will examine what one appropriate analogue is for infinite dimensional systems. A general definition approach will be given motivated by the desire to consider numerical methods. Specific examples illustrating several kinds of behavior will be considered in some detail. It is seen that our definition differs from purely algebraic definitions. Numerical solutions, and simulation difficulties, can be misinterpreted if this index information is missing. 相似文献
10.
N Luca 《Journal of Mathematical Analysis and Applications》1979,67(2):323-339
Various stability types, analogous to those in the theory of ordinary differential equations, are defined for some classes of integrodifferential systems of equations with infinite delays. Then, on the basis of a variation of constants formula and some results in functional analysis and Laplace transform theory, some necessary conditions and necessary and sufficient conditions are established in order that the trivial solution of a class of systems may be classified as one of the stability types considered in the definitions. 相似文献
11.
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of order min{$1/2, \hat{p}$} under the Lipschitz condition and the linear growth condition, where $\hat{p}$ is the exponent of Hölder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter $p$ the derived method can have a better stability property than more commonly used numerical methods. That is, for some $p$, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters $p$. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient. 相似文献
12.
《Numerical Functional Analysis & Optimization》2012,33(3):294-321
AbstractThis article is about Ulam’s type stability of nth order nonlinear differential equations with fractional integrable impulses. It is a best procession to the stability of higher order fractional integrable impulsive differential equations in quasi–normed Banach space. Different Ulam’s type stability results are obtained by using the definitions of Riemann–Liouville fractional integral, Hölder’s inequality and the beta integral inequality. 相似文献
13.
Jia-Chang Sun & Ken Jackson 《计算数学(英文版)》1983,1(3):264-281
A general theory for nonlinear implicit one-step schemes for solving initial value problems for ordinary differential equations is presented in this paper. The general expansion of "symmetric" implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. Based on previous work of the first author on a generalization of means, a fourth-order nonlinear implicit one-step scheme is presented for solving equations with steep gradients. Also, a hybrid method based on the GMS and a fourth-order linear scheme is discussed. Some numerical results are given. 相似文献
14.
Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractionalorder dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system. 相似文献
15.
Brian Straughan 《Annali di Matematica Pura ed Applicata》1980,126(1):187-207
Summary A new type of wave behaviour is found for third order waves in a compressible inviscid dipolar fluid. Several stability-like results are presented for the theories of a viscous incompressible dipolar fluid and a mixture of two viscous incompressible fluids. 相似文献
16.
Pierluigi Amodio Francesca Mazzia 《Journal of Difference Equations and Applications》2013,19(4):353-367
A boundary value appraoch to the numerical solution of initial value problems by means of linear multistep methods is presented. This theory is based on the study of linear difference equations when their general solution is computed by imposing boundary conditions. All the main stability and convergence properties of the obtained methods are investigated abd compared to those of the classical multistep methods. Then, as an example, new itegration formulas, called extended trapezoidal rules, are derived. For any order they have the same stability properties (in the sense of the definitions given in this paper) of the trapezoidal rule, which is the first method in this class. Some numerical examples are presented to confirm the theoretical expectations and to allow us to trust a future code based on boundary value methods. 相似文献
17.
In this paper we design a class of general split-step balanced methods for solving It? stochastic differential systems with m-dimensional multiplicative noise, in which the drift or deterministic increment function can be taken from any chosen one-step ODE solver. We then give an analysis of their order of strong convergence in a general setting, but for the mean-square stability analysis, we confine our investigation to a special case in which the drift increment function of the methods is replaced by the one from the well known Rosenbrock method. The resulting class of stochastic differential equation (SDE) solvers will have more appropriate and useful mean-square stability properties for SDEs with stiffness in their drift and diffusion parts, compared to some other already reported split-step balanced methods. Finally, numerical results show the effectiveness of these methods. 相似文献
18.
D. V. Portnyagin 《Siberian Mathematical Journal》2012,53(2):291-300
We propose a method of generalizing the well-known maximum and comparison principles to nondiagonal parabolic systems of second
order nonlinear differential equations. Under consideration are the cases of Dirichlet and Neumann problems. We also present
some examples of the systems that this method applies to. 相似文献
19.
Peter Burmeister 《Algebra Universalis》1982,15(1):306-358
In this survey, with no proofs included, we collect some material scattered through recent papers and a planned monograph,
which shows that partial algebras do have a two-valued first order model theory which is simpler and nicer than one might
have expected it to be. In section 1 we comment and present some basic definitions. In section 2 a correct and complete two-valued
first order logic is developed. In section 3 the three main concepts of “varieties” are presented, while sections 4 and 5
contain some additional axiomatizability results and some applications, respectively. Section 6 contains some additional remarks.
Presented by E. Fried. 相似文献
20.
A new method for systems stability analysis is presented. This method is called weight functions method and it replaces the problem of Liapunov function finding with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are not general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to found. Conditions of solution stability for linear and nonlinear systems and some examples are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献