Approximation of neutral delay-differential equations

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Catherine Ann Payne (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Richard Fabiano

Abstract: [Mathematical notation cannot be correctly represented here; please see PDF below for full equations.] We study questions related to stability and approximation of the system of linear neutral delay differential equations [equation] with appropriate initial data. Here [A, B subscript 1, B subscript 2,..., B subscript n and C subscript 1, C subscript 2,..., C subscript n] are complex [m x m] matrices for a natural number [m] and [r subscript 1, r subscript 2,... r subscript n] are positive numbers. We construct a new delay-independent sufficient condition for exponential stability of the solution semigroup associated with this equation. We obtain our condition by using the idea of renorming the state space to obtain a strong dissipative inequality on the generator of the solution semigroup. We also construct a new semidiscrete approximation scheme which yields convergence for both the solution semigroup and its adjoint. Finally, we discuss several examples to compare our results with existing results in the literature.

Additional Information

Language: English
Date: 2017
Approximation, Delay equation, Differential equation, Neutral, Semigroup, Stability
Delay differential equations
Approximation theory

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