One-step methods for neutral delay-differential equations with state dependent delays

Z. Jackiewicz

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

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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.

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Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.

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

Guang-Da Hu, Lizhen Shao (2020)

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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

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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...

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