Differential quadrature and Adomian decomposition methods for solving thermal vibration of Euler nanobeam resting on Winkler–Pasternak foundation

2021 ◽  
Vol 16 (4) ◽  
pp. 555-572
Author(s):  
Somnath Karmakar ◽  
Snehashish Chakraverty
Keyword(s):  
Decomposition Methods ◽  
Differential Quadrature ◽  
Thermal Vibration ◽  
Pasternak Foundation ◽  
Adomian Decomposition

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.

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

EXACT SOLUTION OF VAN DER POL NONLINEAR OSCILLATORS ON FINITE DOMAIN BY PADE APPROXIMANT AND ADOMIAN DECOMPOSITION METHODS

2021 ◽  
Vol 10 (6) ◽  
pp. 2755-2766
Author(s):  
E.U. Agom ◽  
F.O. Ogunfiditimi
Keyword(s):  
Exact Analytical Solution ◽  
Adomian Decomposition Method ◽  
Nonlinear Oscillators ◽  
Decomposition Methods ◽  
Padé Approximant ◽  
Finite Domain ◽  
Van Der Pol ◽  
Pade Approximant ◽  
Adomian Decomposition ◽  
The Given

This paper is concerned with a thorough investigation in achieving exact analytical solution for the Van der Pol (VDP) nonlinear oscillators models via Adomian decomposition method (ADM). The models are nonlinear time dependent second order ordinary differential equations. ADM has already been applied, in existing literatures, to obtain approximate results. But, we adapt the method by adjusting the source term; a procedure that is base on the asymptotic Taylor's series expansion on the term that would have resulted to proliferation of terms during the invertible process. Then, the rational Pade Approximant is applied to clarify and get a better understanding of the uniqueness and convergence of our findings. Two models were used as illustrations and their result pictured to indicate their behaviour in the given domains. And, we found that the adaptation on the models yielded exact results which were further displayed in constructed tables.

scholarly journals Comparison of Optimal Homotopy Asymptotic and Adomian Decomposition Methods for a Thin Film Flow of a Third Grade Fluid on a Moving Belt

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Grade Fluid

We have investigated a thin film flow of a third grade fluid on a moving belt using a powerful and relatively new approximate analytical technique known as optimal homotopy asymptotic method (OHAM). The variation of velocity profile for different parameters is compared with the numerical values obtained byRunge-Kutta Fehlberg fourth-fifth ordermethod and with Adomian Decomposition Method (ADM). An interesting result of the analysis is that the three terms OHAM solution is more accurate than five terms of the ADM solution and this thus confirms the feasibility of the proposed method.

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