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Open AccessArticle

Approximation of a Linear Autonomous Differential Equation with Small Delay

1
Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, Corunca, 547367 Mures, Romania
2
Department of Mathematics, University of Pannonia, 8200 Veszprém, Hungary
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1299; https://doi.org/10.3390/sym11101299
Received: 30 September 2019 / Revised: 10 October 2019 / Accepted: 12 October 2019 / Published: 15 October 2019
A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary differential equation is a solution of an associated matrix equation and it can be written as a limit of a sequence of matrices obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the dominant characteristic roots of the delay differential equation and an explicit estimate for the approximation error is given. View Full-Text
Keywords: delay differential equation; ordinary differential equation; asymptotic equivalence; approximation; eigenvalue delay differential equation; ordinary differential equation; asymptotic equivalence; approximation; eigenvalue
MDPI and ACS Style

Fehér, Á.; Márton, L.; Pituk, M. Approximation of a Linear Autonomous Differential Equation with Small Delay. Symmetry 2019, 11, 1299.

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