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.

THE NEW ADM–PADÉ TECHNIQUE FOR THE GENERALIZED EMDEN–FOWLER EQUATIONS

2010 ◽  
Vol 24 (12) ◽  
pp. 1237-1254 ◽  
Author(s):  
HONGMEI CHU ◽  
YINPING LIU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Padé Approximant ◽  
Convergence Domain ◽  
Adomian Polynomials ◽  
Solution Series ◽  
Pade Approximant ◽  
Adomian Decomposition ◽  
New Type

In this paper, the Emden–Fowler equations are investigated by employing the Adomian decomposition method (ADM) and the Padé approximant. By using the new type of Adomian polynomials proposed by Randolph C. Rach in 2008, our obtained solution series converges much faster than the regular ADM solution of the same order. Meanwhile, we note that the solutions obtained by using the new ADM–Padé technique have much higher accuracy and larger convergence domain than those obtained by using the regular ADM together with the Padé technique. Finally, comparison of our new obtained solutions are given with those existing exact ones graphically to illustrate the validity and the promising potential of the new ADM–Padé technique for solving nonlinear problems.

A New Algorithm on the Solutions of Forced Convective Heat Transfer in a Semi-Infinite Flat Plate

2011 ◽  
Vol 27 (1) ◽  
pp. 63-69 ◽  
Author(s):  
P.-Y. Tsai ◽  
C.-K. Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Decomposition Method ◽  
Thermal Boundary Layer ◽  
Adomian Decomposition Method ◽  
Padé Approximant ◽  
Temperature Fields ◽  
Pade Approximant ◽  
Adomian Decomposition

ABSTRACTIn this paper, a new algorithm is proposed to solve the velocity and temperature fields in the thermal boundary layer flow over a semi-infinite flat plate. Both the flow and heat transfer solutions are calculated accurately by the Laplace Adomian decomposition method, Padé approximant and the optimal design concept. The Laplace Adomian decomposition method (LADM) is a combination of the numerical Laplace transform algorithm with the Adomian decomposition method (ADM). A hybrid method of the LADM combined with the Padé approximant, named the LADM-Padé approximant technique, is introduced to solve the thermal boundary layer problems directly without any small parameter assumptions, linearizatons or transformations of the boundary value problems to a pair of initial value problems. The LADM-Padé approximant solutions here in are given to show the accuracy in comparison with different method solutions.

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 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.

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.

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.

scholarly journals Behaviour Analysis of the Padé Sumudu Adomian Decomposition Method Solution

2021 ◽  
pp. 39-45
Author(s):  
Richard Metonou ◽  
Zhao Weidong
Keyword(s):  
Decomposition Method ◽  
Schrodinger Equation ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Pade Approximation ◽  
Approximation Solution ◽  
Behaviour Analysis ◽  
The Past ◽  
Adomian Decomposition

Researchers in the past investigate the Sumudu Adomian Decomposition Method (SADM), the Laplace Adomian Decomposition Method (LADM), the Padé Sumudu Adomian Decomposition Methods (PSADM). In this paper we analyse the behaviour of the function P[L/M][.] called double Padé approximation using in the Padé Sumudu Adomian Decomposition Method (PSADM), and provide some criteriums for chosing L and M to obtain the best Padé approximation solution in the case of nonlinear Schrödinger equation and nonlinear KdV Burger's equation.

scholarly journals An Investigation on an Optimal Control Problem with a Fractional Constraint in the Riemann-Liouville Sense

2016 ◽  
Vol 7 ◽  
pp. 10-18
Author(s):  
Mehdi Nategh ◽  
Bahram Agheli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Adomian Decomposition Method ◽  
Auxiliary Variable ◽  
Analytic Description ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Sufficient And Necessary Conditions ◽  
The Given

This work, deals with a fractional optimal control problem (in the Riemann-Liouville sense). An analytic description of an initial value appears in the constraint of the optimal control problem is presented and some sufficient and necessary conditions for the given initial value is obtained. Making use of an auxiliary variable together with the optimal control law, the given problem is converted into a system of ordinary integro-differential equations. Then using the Adomian decomposition method, an approximate solution is illustrated.

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