The comparison of the stability of Adomian decomposition method with numerical methods of equation solution

2007 ◽  
Vol 186 (1) ◽  
pp. 665-669 ◽  
Author(s):  
A. Aminataei ◽  
S.S. Hosseini
Keyword(s):  
Numerical Methods ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Equation Solution ◽  
Adomian Decomposition ◽  
The Stability

scholarly journals Using Adomian decomposition method for solving a vector-host model

2016 ◽  
Vol 5 (2) ◽  
pp. 107
Author(s):  
Ibrahim Elmojtaba
Keyword(s):  
Numerical Methods ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Runge Kutta

In this paper, we use Adomian decomposition method (ADM) for solving a vector-host model by using an alternate algorithm suggested by Biazar et. al [4]. Some of the first terms were generated and plotted against time and compared our results with the regular Runge-Kutta numerical methods by using Matlab ode45 function.

scholarly journals On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

2021 ◽  
Vol 7 (3) ◽  
pp. 4552-4573
Author(s):  
Saima Rashid ◽  
◽  
Fahd Jarad ◽  
Fatimah S. Bayones ◽  
◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Decomposition Method ◽  
Disease Model ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Sir Epidemic Model ◽  
Childhood Diseases ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
The Stability

<abstract><p>The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.</p></abstract>

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

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