Application of optimal homotopy asymptotic method for solving linear delay differential equations

2013 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Asymptotic Method ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
Optimal Homotopy Asymptotic Method ◽  
Delay Differential

scholarly journals Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Asymptotic Method ◽  
Delay Differential Equations ◽  
Perturbation Methods ◽  
Analytic Solution ◽  
Approximate Analytic Solution ◽  
Initial Value ◽  
Optimal Homotopy Asymptotic Method ◽  
Delay Differential ◽  
First Time

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

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
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