Displaying similar documents to “One-step methods for neutral delay-differential equations with state dependent delays”

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

Similarity:

A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.

Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

On oscillation of a kind of integro-differential equation with delay

Binggen Zhang (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

This note contains a criterion for the oscillation of solution of a kind of integro-differential equations with delay.

Delay-dependent stability of linear multi-step methods for linear neutral systems

Guang-Da Hu, Lizhen Shao (2020)

Kybernetika

Similarity:

In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. Combining with Lagrange interpolation, linear multi-step methods can be applied to the neutral systems. Utilizing the argument principle, a sufficient condition...

Delay-dependent stability of high-order neutral systems

Yanbin Zhao, Guang-Da Hu (2021)

Kybernetika

Similarity:

In this note, we are concerned with delay-dependent stability of high-order delay systems of neutral type. A bound of unstable eigenvalues of the systems is derived by the spectral radius of a nonnegative matrix. The nonnegative matrix is related to the coefficient matrices. A stability criterion is presented which is a necessary and sufficient condition for the delay-dependent stability of the systems. Based on the criterion, a numerical algorithm is provided which avoids the computation...