scholarly journals Asymptotic behaviour of solutions of some linear delay differential equations

2000 ◽  
Vol 125 (3) ◽  
pp. 355-364
Author(s):  
Jan Čermák
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Delay Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Linear Delay ◽  
Delay Differential

Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations

1998 ◽  
Vol 128 (6) ◽  
pp. 1371-1387 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Characteristic Equation ◽  
Trivial Solution ◽  
Delay Differential Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Delay ◽  
The Stability ◽  
Delay Differential

First-order scalar linear delay differential equations with periodic coefficients and constant delays are considered, where the coefficients have a common period and the delays are multiples of this period. A basic asymptotic criterion is given. Moreover, some results on the nonoscillation and on the stability of the trivial solution are obtained. An equation, which is in a sense the characteristic equation, plays an important role in establishing the results of the paper.

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.

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