Abstract
In this paper, a multi-term nonlinear delay differential equation (DDE) of arbitrary order is studied.Adomian decomposition method (ADM) is used to solve these types of equations. Then the existence andstability of a unique solution will be proved. Convergence analysis of ADM is discussed. Moreover, themaximum absolute truncated error of Adomian’s series solution is estimated. The stability of the solutionis also discussed.
Highlights
Differential equations of arbitrary orders and delay differential equations (DDEs) have many applications in engineering and science, including electrical networks, fluid flow, control theory, fractals theory, electromagnetic theory, viscoelasticity, potential theory, chemistry, biology, optical and neural network systems with delayed feedback [1][19]
The paper is organized as follows: In section two Adomian decomposition method (ADM) is applied to the problem under consideration
When we have compared the ADM solution with the exact solution, we have seen that it gives a good approximate solution and it is enclosed with the results obtained from using Theorem 3
Summary
Differential equations of arbitrary orders and delay differential equations (DDEs) have many applications in engineering and science, including electrical networks, fluid flow, control theory, fractals theory, electromagnetic theory, viscoelasticity, potential theory, chemistry, biology, optical and neural network systems with delayed feedback [1][19]. Adomian decomposition method (ADM) [20]-[26] is used to solve nonlinear fractional delay differential equations (FDDEs). This method has many advantages; it is efficiently works with different types of linear and nonlinear equations in deterministic or stochastic fields and gives an analytic solution for all these types of equations without linearization or discretization. The paper is organized as follows: In section two ADM is applied to the problem under consideration. Convergence; error analysis and stability are discussed. Two numerical examples are presented by using MATHEMATICA package. E.A.A. Ziada / Numerical solution for multi-term fractional delay differential
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