Discussion: “Analysis of a System of Linear Delay Differential Equations” (Asl, F. M., and Ulsoy, A. G., 2003, ASME J. Dyn. Syst., Meas., Control, 125, pp. 215–223)

2007 ◽  
Vol 129 (1) ◽  
pp. 121-122 ◽  
Author(s):  
Naci Zafer
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
Delay Differential

This work presents a commentary of the article published by Asl and Ulsoy (2003, ASME J. Dyn. Syst., Meas., Control, 125, pp. 215–223). We show by an example that their method leads to inaccurate results and is therefore erroneous.

scholarly journals An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Süleyman Cengizci
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Numerical Procedure ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Singularly Perturbed ◽  
Convection Term ◽  
Linear Delay ◽  
Delay Differential

In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.

scholarly journals Notes on oscillation of linear delay differential equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Božena Dorociaková ◽  
Radoslav Chupáč ◽  
Rudolf Olach
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms

2019 ◽  
Vol 69 (5) ◽  
pp. 1117-1126
Author(s):  
Said R. Grace ◽  
John R. Graef ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Linear Delay ◽  
Delay Differential

Abstract This article concerns the oscillatory behavior of solutions to second-order half-linear delay differential equations with mixed neutral terms. The authors present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated with examples.

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