Adomian decomposition method for a reliable treatment of the Bratu-type equations

Wazwaz, Abdul‐Majid

doi:10.1016/j.amc.2004.06.059

Cited by 204 publications

(154 citation statements)

References 8 publications

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“…H s ptq " However, replacing the above solution in system (15) and including the embedding parameter p P p0, 1s, putting together all the terms of the same power of the embedding parameter p we obtain:…”

Section: Solution With the Homotopy Decomposition Methodsmentioning

confidence: 99%

“…That is why in the recent decades, several studies have been done in order to build some analytical techniques that can be used to provide asymptotic solutions in such systems. We shall mention some of the recent and efficient ones that have been intensively used, such as the homotopy perturbation method [11,13], the Adomian Decomposition method [14,15], the homotopy Laplace perturbation method [16], the Sumudu homotopy perturbation method [17] and the homotopy decomposition method [18]. However, in this paper we shall use only two of these mentioned techniques, namely the Laplace homotopy perturbation method and the homotopy decomposition method.…”

Section: Analysis Of Approximate Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Atangana

Alqahtani

2016

Entropy

125

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Abstract:Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations.

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Section: Solution With the Homotopy Decomposition Methodsmentioning

confidence: 99%

Section: Analysis Of Approximate Solutionsmentioning

confidence: 99%

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Atangana

Alqahtani

2016

Entropy

125

View full text Add to dashboard Cite

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“…In addition, it is not guaranteed that a perturbation result is valid in the whole region of all physical parameters. In order to overcome the restrictions of perturbation techniques, some non perturbation methods are developed, such as Lyapunov's artificial small parameter method (Liao, 2003;Abbasbandy, 2006) the Adomian decomposition method (Wazwaz, 2005Bildik & Konuralp, 2006 and so on. In general, all these methods are based on a so-called artificial parameter, and the approximation of solutions are due to series with the artificial small parameter.…”

Section: Homotopy Analysis Methods (Ham)mentioning

confidence: 99%

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

Nave¹,

Ajadi²,

Gol’dshtein³

2016

APR

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In the present paper we applied two well-known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter ℏ. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions. γ (conventional parameter of Semenov's theory of thermal explosion), the final dimensionless adiabatic temperature of the thermally insulated system after explosion. This parameter is small compared with unity for most gaseous mixture due to the high exothermicity and activation energy of the chemical reactionwhere ϵ d is the emissivity of the droplet surface ϵ 1,2 dimensionless parameters, introduced for the first time (Gol'dshtein, Goldfarb, Shreiber, & Zinoviev, 1996) and describe the relations between the thermo physical properties of the gas and liquid phases

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“…These methods have aided in obtaining approximate solutions to a wide class of linear and nonlinear differential equations [1,9,10,11,14,23,24,25,27,29,30,38,40]. However, only a few papers deal with the comparison of these methods [2,26,41].…”

Section: Introductionmentioning

confidence: 99%

A Comparison of the Adomian and Homotopy Perturbation Methods in Solving the Problem of Squeezing Flow Between Two Circular Plates

Siddiqui

Haroon

Bhatti

et al. 2010

Mathematical Modelling and Analysis

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Abstract. The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier-Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench-marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

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Adomian decomposition method for a reliable treatment of the Bratu-type equations

Cited by 204 publications

References 8 publications

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

A Comparison of the Adomian and Homotopy Perturbation Methods in Solving the Problem of Squeezing Flow Between Two Circular Plates

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