Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method

Abbasbandy, Saeid

doi:10.1016/j.cej.2007.03.022

Cited by 165 publications

(77 citation statements)

References 25 publications

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“…The HAM has been successfully applied by many researchers for solving linear and nonlinear partial differential equations. [14][15][16][17][18][19][20][21][22] In recent years, many researchers have paid attention to obtaining solutions to linear and nonlinear differential and integral equations using various methods by combining the Laplace transform method. Among these, we may mention the following: Laplace decomposition methods 23,24 and homotopy perturbation transform method.…”

Section: Introductionmentioning

confidence: 99%

A modified homotopy analysis method for solution of fractional wave equations

Yin

Kumar

2015

Advances in Mechanical Engineering

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The aim of this article is to introduce a modified analytical approach to obtain quick and accurate solution of wave-like fractional physical models. This modified analytical approach is an innovative adjustment in Laplace transform algorithm and homotopy analysis method for fractional partial differential equations. The proposed technique solves the problems using Adomian's polynomials. The homotopy analysis transform method utilizes a simple and powerful method to adjust and control the convergence region of the infinite series solution using an auxiliary parameter. The numerical solutions obtained by this modified proposed method indicate that the approach is easy to implement, highly accurate, and computationally very attractive. A good agreement between the obtained solutions and some well-known results has been obtained.

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Section: Introductionmentioning

confidence: 99%

A modified homotopy analysis method for solution of fractional wave equations

Yin

Kumar

2015

Advances in Mechanical Engineering

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“…The results reveal that the method is very effective and simple. The method contains the auxiliary parameter ℎ, which provides us with a simple way to adjust and control the convergence region of solution series [15,16]. Homotopy analysis method provides a powerful tool to strongly analyze linear and nonlinear problems [17,18].…”

Section: Concentrations Of Native Enzyme Form Denatured Enzyme Formmentioning

confidence: 99%

Mathematical Modeling and Analysis of the Kinetics of Thermal Inactivation of Enzyme

Ananthi¹,

Manimozhi²,

Praveen³

et al. 2013

International Journal of Engineering Mathematics

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A theoretical model of Illeova et al. (2003) thermal inactivation of urease is discussed. Analytical expressions pertaining to the molar concentrations of the native and denatured enzyme are obtained in terms of second-order reaction rate constant. Simple and closed form of theoretical expression pertains to the temperature are also derived. In this paper, homotopy analysis method (HAM) is used to obtain approximate solutions for a nonlinear ordinary differential equation. The obtained approximate result in comparison with the numerical ones is found to be in satisfactory agreement.

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“…The Homotopy Analysis Method (HAM) which first proposed in 1992 by liao [11] is successful method to find the exact analytical solutions for linear and nonlinear problem. This method has been successfully applied into physics, chemical, biology, engineering fields and science [12][13][14][15][16]. In this paper, we present a solution of a more general model of an enzyme-catalyzed reaction model:…”

Section: Introductionmentioning

confidence: 99%

An Application of the Homotopy Analysis Method to the Transient Behavior of a Biochemical Reaction Model

Arafa¹,

Rida²,

Mohamed³

2014

Inf. Sci. Lett.

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Abstract:In this paper, the homotopy analysis method (HAM) is applied to solve fractional transient phase of the Michaelis-Menten reaction. The analytical solution, which is given in the form of a power series, is found to be highly accurate in predicting the behavior of the reaction in the very early stages. The fractional derivatives are described by Caputo's sense. We also present a comparison of the various analytical approximations and a direct numerical solution of this problem. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.

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Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method

Cited by 165 publications

References 25 publications

A modified homotopy analysis method for solution of fractional wave equations

A modified homotopy analysis method for solution of fractional wave equations

Mathematical Modeling and Analysis of the Kinetics of Thermal Inactivation of Enzyme

An Application of the Homotopy Analysis Method to the Transient Behavior of a Biochemical Reaction Model

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