Analytical treatment and convergence of the Adomian decomposition method for a system of coupled damped wave equations

Rajaram, Rajeev; Najafi, M.

doi:10.1016/j.amc.2009.02.006

Cited by 14 publications

(9 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [23,24], convergence was investigated when the method applied to a general functional equations and to specific type of equations in [25,26]. In convergence analysis, Adomian's polynomials play a very important role which could affect directly on the accuracy as well as the convergence rate.…”

Section: Convergence Analysismentioning

confidence: 99%

Piece-wise continuous solution to a class of nonlinear boundary value problems

El‐Kalla

2013

Ain Shams Engineering Journal

View full text Add to dashboard Cite

show abstract

Section: Convergence Analysismentioning

confidence: 99%

Piece-wise continuous solution to a class of nonlinear boundary value problems

El‐Kalla

2013

Ain Shams Engineering Journal

View full text Add to dashboard Cite

show abstract

“…In [25,26], convergence was investigated when the method applied to a general functional equations and to specific type of equations in [27,28]. In convergence analysis, Adomian's polynomials play a very important role however, these polynomials cannot utilize all the information concerning the obtained successive terms of the series solution, which could affect directly the accuracy as well as the convergence region and the convergence rate.…”

Section: Convergence Analysismentioning

confidence: 99%

Error estimates for series solutions to a class of nonlinear integral equations of mixed type

El‐Kalla

2011

J. Appl. Math. Comput.

View full text Add to dashboard Cite

In this paper, we prove that the accelerated Adomian polynomials formula suggested by Adomian (Nonlinear Stochastic Systems: Theory and Applications to Physics, Kluwer, Dordrecht, 1989) and the accelerated formula suggested by El-Kalla (Int. J. Differ. Equs. Appl. 10(2):225-234, 2005; Appl. Math. E-Notes 7: [214][215][216][217][218][219][220][221] 2007) are identically the same. The Kalla-iterates exhibit the same faster convergence exhibited by Adomian's accelerated iterates with the additional advantage of absence of any derivative terms in the recursion, thereby allowing for ease of computation. Moreover, the formula of El-Kalla is used directly to prove the convergence of the series solution to a class of nonlinear two dimensional integral equations. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the Adomian series solution.

show abstract

“…Rigorous proof of the convergence of the series solution has been dealt with in [13]- [16] and these theorems will not be repeated here. To compute the irreversibility ratio for the heat flow, we set…”

Section: Methods Of Solutionmentioning

confidence: 99%

Thermodynamics Analysis for a Reacting Couple Stress Fluid Flow Through a Vertical Channel

Adesanya¹,

Falade²,

Ukaegbu³

et al. 2017

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

In this paper, entropy generation rate in the flow of couple stress fluid undergoing exothermic chemical reaction through a porous vertical channel is studied by applying the second law of thermodynamics. A semi-analytical solution for the governing equations is obtained using Adomian decomposition method (ADM). The effects of couple stress parameter, internal heat generation parameter, Dufour number on the velocity, temperature distribution, entropy generation rate and Bejan number are investigated and the results were presented graphically. The results show that solutal diffusivity has significant effect on the entropy generation rate and irreversibility of heat in a couple stress fluid flow.

show abstract

Analytical treatment and convergence of the Adomian decomposition method for a system of coupled damped wave equations

Cited by 14 publications

References 5 publications

Piece-wise continuous solution to a class of nonlinear boundary value problems

Piece-wise continuous solution to a class of nonlinear boundary value problems

Error estimates for series solutions to a class of nonlinear integral equations of mixed type

Thermodynamics Analysis for a Reacting Couple Stress Fluid Flow Through a Vertical Channel

Contact Info

Product

Resources

About