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1.
There are few results on the numerical stability of nonlinear neutral stochastic delay differential equations (NSDDEs). The aim of this paper is to establish some new results on the numerical stability for nonlinear NSDDEs. It is proved that the semi-implicit Euler method is mean-square stable under suitable condition. The theoretical result is also confirmed by a numerical experiment. 相似文献
2.
非线性时滞差分议程的全局渐近稳定性 总被引:1,自引:0,他引:1
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed. 相似文献
3.
Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation 总被引:16,自引:0,他引:16
Mingzhu Liu Wanrong Cao Zhencheng Fan 《Journal of Computational and Applied Mathematics》2004,170(2):123-268
The paper deals with convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. It is proved that the semi-implicit Euler method is convergent with strong order
. The conditions under which the method is MS-stable and GMS-stable are determined and the numerical experiments are given. 相似文献
4.
本讨论非线性变延迟微分方程隐式Euler法的渐近稳定性。我们证明,在方程真解渐近稳定的条件下,隐式Euler法也是渐近稳定的。 相似文献
5.
1.IntroductionPartialdifferenceequationshaveappearedinmanybranchesofmathematics.Indeed,LagrangeandLaplacehavediscussedsuchequationsinrelationtoprobability[1],Couralltetal.[z]haveconsideredtheminrelationtodifferentialequationsofmathematicalphysics.Inrecenty6ars,signalandimageprocessingtheory(seee.g.[3])alsomakesuseofthetheoryofpartialdchrenceequations.OscillationtheoryfortheseeqllationshasbeeninvestigatedbyanUmberofauthorsrecelltly[4].However,asystematicinvestigationofthestabilitytheoryofpart… 相似文献
6.
N. O. Sedova 《Russian Mathematics (Iz VUZ)》2008,52(11):60-69
We study certain sufficient conditions for the local and global uniform asymptotic stability, as well as the stabilizability of the equilibrium in cascade systems of delay differential equations. As distinct from the known results, the assertions presented in this paper are also valid for the cases, when the right-hand sides of equations are nonlinear and depend on time or arbitrarily depend on the historical data of the system. We prove that the use of auxiliary constant-sign functionals and functions with constant-sign derivatives essentially simplifies the statement of sufficient conditions for the asymptotic stability of a cascade. We adduce an example which illustrates the use of the obtained results. It demonstrates that the proposed procedure makes the study of the asymptotic stability and the construction of a stabilizing control easier in comparison with the traditional methods. 相似文献
7.
《Mathematical Methods in the Applied Sciences》2018,41(13):4986-5002
In this paper, we consider the numerical approximation of stochastic partial differential equations with nonlinear multiplicative trace class noise. Discretization is obtained by spectral collocation method in space, and semi‐implicit Euler method is used for the temporal approximation. Our purpose is to investigate the convergence of the proposed method. The rate of convergence is obtained, and some numerical examples are included to illustrate the estimated convergence rate. 相似文献
8.
Genqiang Wang 《Journal of Mathematical Analysis and Applications》2004,298(1):298-307
Existence criteria are proved for the periodic solutions of a first order nonlinear differential equation with piecewise constant arguments. 相似文献
9.
10.
T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise 总被引:1,自引:0,他引:1
Wanrong Cao 《Applied mathematics and computation》2010,216(3):999-1006
The paper deals with the T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise. A difference equation is obtained by applying the numerical method to a linear test equation, in which the Wiener increment is approximated by a discrete random variable with two-point distribution. The conditions under which the method is T-stable are considered and the numerical experiments are given. 相似文献
11.
In this paper an explicit numerical difference scheme for mixed problems for the delay diffusion equation is proposed, as a generalization of the classic difference scheme for the diffusion problem. A sufficient condition for the asymptotic stability of the new scheme is proved. Consistence, convergence and some properties of stability for this scheme are studied. Illustrative examples of numerical results are also included. 相似文献
12.
13.
M. M. Lafisheva M. Kh. Shkhanukov-Lafishev 《Computational Mathematics and Mathematical Physics》2008,48(10):1875-1884
Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved. 相似文献
14.
Bhargav Kumar Kakumani Suman Kumar Tumuluri 《Mathematical Methods in the Applied Sciences》2016,39(4):697-708
In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
15.
本文讨论了一类Rosenbrock方法求解比例延迟微分方程,y′(t)=λy(t) μy(qt),λ,μ∈C,0 相似文献
16.
Shoufu LI 《Frontiers of Mathematics in China》2009,4(1):23-48
In this review, we present the recent work of the author in comparison with various related results obtained by other authors
in literature. We first recall the stability, contractivity and asymptotic stability results of the true solution to nonlinear
stiff Volterra functional differential equations (VFDEs), then a series of stability, contractivity, asymptotic stability
and B-convergence results of Runge-Kutta methods for VFDEs is presented in detail. This work provides a unified theoretical foundation
for the theoretical and numerical analysis of nonlinear stiff problems in delay differential equations (DDEs), integro-differential
equations (IDEs), delayintegro-differential equations (DIDEs) and VFDEs of other type which appear in practice.
相似文献
17.
C. Gonzá lez A. Ostermann C. Palencia M. Thalhammer. 《Mathematics of Computation》2002,71(237):125-145
This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further show that the geometric properties near a hyperbolic equilibrium are well captured by the discretization. A numerical example is given.
18.
In the paper, we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses
19.
In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Fory? (Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
20.
We present the Riemann–Hilbert problem formalism for the initial value problem for the Hirota equation on the line. We show that the solution of this initial value problem can be obtained from that of associated Riemann–Hilbert problem, which allows us to use nonlinear steepest descent method/Deift–Zhou method to analyze the long-time asymptotic for the Hirota equation. 相似文献