scholarly journals Solution of a Nonlinear Delay Differential Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomial

2019 ◽  
Vol 09 (04) ◽  
pp. 221-233
Author(s):  
I. L. El-Kalla ◽  
Khaled M. Abd Elgaber ◽  
Ali R. Elmahdy ◽  
Ahmed Y. Sayed
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Adomian Polynomial ◽  
Nonlinear Delay

scholarly journals Application of the Decomposition Method of Adomian for Solving the Pantograph Equation of Order m

2010 ◽  
Vol 65 (5) ◽  
pp. 453-460 ◽  
Author(s):  
Fatemeh Shakeri ◽  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Rate Of Change ◽  
System Delay ◽  
Pantograph Equation ◽  
Adomian Decomposition ◽  
Relevant Role ◽  
Delay Differential

In many fields of the contemporary science and technology, systems with delaying links often appear. By a delay differential equation (DDE), we mean an evolutionary system in which the (current) rate of change of the state depends on the historical status of the system. Delay models play a relevant role in different fields such as biology, economy, control, and electrodynamics and hence have been attracted a lot of attention of the researchers in recent years. In this study, the numerical solution of a well-known delay differential equation, namely, the pantograph equation is investigated by means of the Adomian decomposition method and then a numerical evaluation is included to demonstrate the validity and applicability of this procedure

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

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