Results 31 to 40 of about 173,435,843 (136)
The asymptotic stability of difference equations
Applied Mathematics Letters, 2000 The paper discusses the stability properties of the linear delay difference equation \[ x_{n+1}-x_n=-a_nx_{n-k} , \tag{1} \] where \(a_n\geq 0\) and \(k\geq 1\). As the main result it is proved that if \[ \sum_{n=0}^{\infty}a_n=\infty \tag{"(C1)"} \] and \[ \underset{n\to\infty}\limsup \sum_{j=n-2k}^{n-1 ...
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Backward difference replacements of the space derivative in first order hyperbolic equations [PDF]
, 1983 Two families of two-time level difference schemes are developed for the numerical solution of first order hyperbolic partial differential equations with one space variable.
Khaliq, AQM, Twizell, EH
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Asymptotic Stability for a Class of Nonlinear Difference Equations
Discrete Dynamics in Nature and Society, 2010 We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a)
Chang-you Wang +4 more
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Global asymptotic stability of solutions of cubic stochastic difference equations
Advances in Difference Equations, 2004 Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven under appropriate conditions ...
Henri Schurz, Alexandra Rodkina
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Stability of Solutions for a Family of Nonlinear Difference Equations
Advances in Difference Equations, 2008 We consider the family of nonlinear difference equations: , , where for , , and the initial values . We give sufficient conditions under which the unique equilibrium of these equations is globally asymptotically stable, which extends and ...
Sun Taixiang, Xi Hongjian, Han Caihong
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On the Stability of Volterra Difference Equations of Convolution Type
Trends in Computational and Applied Mathematics, 2018 In \cite{Elaydi-10}, S.\ Elaydi obtained a characterization of the stability of the null solution of the Volterra difference equation \beqae x_n=\sum_{i=0}^{n-1} a_{n-i} x_i\textrm{,}\quad n\geq 1\textrm{,} \eeqae by localizing the roots of its ...
Higidio Portillo Oquendo +2 more
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CRITERIA FOR STABILITY OF VOLTERRA DIFFERENCE EQUATIONS
Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics", 2020 Summary: Continuous and discrete Volterra-type difference equations arise in many applications. In particular, when studying models of population dynamics, modeling various economic or physical processes, in management theory, and medicine. The paper deals with the problem of asymptotic stability of the zero solution of a linear difference equation of ...
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Complexity, 2022 In this paper, we study the uniqueness and existence of the solutions of four types of non-singular delay difference equations by using the Banach contraction principles, fixed point theory, and Gronwall’s inequality.
Sawitree Moonsuwan +5 more
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On the stability of differential-difference equations [PDF]
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1976 AbstractThe local properties of non-linear differential-difference equations are investigated by considering the location of the roots of the eigen-equation derived from the lineraised approximation of the original model. A general linear system incorporating one time delay is considered and local stability results are obtained for cases in which the ...
Braddock, R. D., van den Driessche, P.
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Global Asymptotic Stability of a Family of Nonlinear Difference Equations
Discrete Dynamics in Nature and Society, 2013 In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, where ki∈ℕ (i=1,2,…,v), v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-
Maoxin Liao
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