Journal ArticleDOI
A stability property ofA-stable natural Runge-Kutta methods for systems of delay differential equations
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TLDR
This paper considers a linear constant-coefficient system of DDEs with a constant delay, and shows that anA-stable method preserves the asymptotic stability property of the analytical solutions of the system.Abstract:
A natural Runge-Kutta method is a special type of Runge-Kutta method for delay differential equations (DDEs); it is known that any one-step collocation method is equivalent to one of such methods. In this paper, we consider a linear constant-coefficient system of DDEs with a constant delay, and discuss the application of natural Runge-Kutta methods to the system. We show that anA-stable method preserves the asymptotic stability property of the analytical solutions of the system.read more
Citations
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On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
Koen Engelborghs,Dirk Roose +1 more
TL;DR: This work investigates the use of linear multistep (LMS) methods for computing characteristic roots of systems of (linear) delay differential equations (DDEs) with multiple fixed discrete delays and proves convergence orders for the characteristic root approximations.
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Stability analysis of numerical methods for systems of neutral delay-differential equations
Guang-Da Hu,Taketomo Mitsui +1 more
TL;DR: In this paper, the stability analysis of some representative numerical methods for systems of neutral delay-differential equations (NDDEs) is considered, after the establishment of a sufficient condition of asymptotic stability for linear NDDEs.
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Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems
Alfredo Bellen,Stefano Maset +1 more
TL;DR: The scheme of discretization is proved to be convergent and the asymptotic stability is investigated for two significant classes of asymPTotically stable problems.
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Stability of Runge-Kutta methods for delay integro-differential equations
TL;DR: In this article, the authors studied the stability of Runge-Kutta (RK) methods for delay integro-differential equations with a constant delay on the basis of the linear equation du/dt = Lu(t) + Mu(t - τ) + K ∫t − τt u(θ)dθ, where L,M,K are constant complex matrices.
Journal ArticleDOI
Asymptotic stability of linear delay differential-algebraic equations and numerical methods
Wenjie Zhu,Linda R. Petzold +1 more
TL;DR: This paper considers the asymptotic stability of linear constant coefficient delay differential-algebraic equations and of &methods, Runge-Kutta methods and linear multistep methods applied to these systems.
References
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Journal ArticleDOI
Natural continuous extensions of Runge-Kutta methods
TL;DR: In this paper, a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given by a Runge-Kutta process is developed.
Journal ArticleDOI
Special stability problems for functional differential equations
TL;DR: In this paper, the stability properties of numerical methods for functional differential equations, similar to A-stability for ordinary differential equations are considered, and definitions are proposed for categories of numerical stability.
Journal ArticleDOI
P-stability properties of runge-kutta methods for delay differential equations
TL;DR: In this article, it is shown that any Astable one-step collocation method for ODEs inherits the same property when it is applied to DDEs with a constrained mesh (i.e. it is P-stable).
Journal ArticleDOI
A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
TL;DR: A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblems U′(t)=λU (t)+μU(t−τ) with λ, μ e C, Re(λ) 0.
Journal ArticleDOI
Stability analysis of numerical methods for delay differential equations
K. J. in 't Hout,M. N. Spijker +1 more
TL;DR: In this paper, the stability analysis of step-by-step methods for the numerical solution of delay differential equations is studied and a general theorem is presented to obtain complete characterizations of the stability regions of these methods.
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