Oscillation, convergence, and stability of linear delay differential equations

2021 ◽  
Vol 293 ◽  
pp. 282-312
Author(s):  
John Ioannis Stavroulakis ◽  
Elena Braverman
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Convergence And Stability ◽  
Linear Delay ◽  
Delay Differential

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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