Homotopy analysis method for singular IVPs of Emden-Fowler type

被引：82

作者：

Bataineh, A. Sami ^{[1
]}

Noorani, M. S. M. ^{[1
]}

Hashim, I. ^{[1
]}

机构：

[1] Univ Kebangsaan Malaysia, Sch Math Sci, Bangi 43600, Selangor, Malaysia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2009年 / 14卷 / 04期

关键词：

Homotopy analysis method; Lane-Emden equation; Emden-Fowler equations; Singular IVPs; APPROXIMATE SOLUTION TECHNIQUE; DECOMPOSITION METHOD; SMALL PARAMETERS; EQUATIONS; EXPLICIT; FLOWS;

D O I：

10.1016/j.cnsns.2008.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, approximate and/or exact analytical solutions of singular initial value problems (IVPs) of the Emden-Fowler type in the second-order ordinary differential equations (ODEs) are obtained by the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. It is shown that the solutions obtained by the Adomian decomposition method (ADM) and the homotopy-perturbation method (HPM) are only special cases of the HAM solutions. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：1121 / 1131

页数：11

共 35 条

[1] Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method [J].

Abbasbandy, S. .

CHEMICAL ENGINEERING JOURNAL, 2008, 136 (2-3) :144-150

[2] The application of homotopy analysis method to nonlinear equations arising in heat transfer [J].

Abbasbandy, S. .

PHYSICS LETTERS A, 2006, 360 (01) :109-113

[3]

ABBASBANDY S, 2006, PHYS LETT A, V15, P1

[4] SOLUTION OF PHYSICAL PROBLEMS BY DECOMPOSITION [J].

ADOMIAN, G .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1994, 27 (9-10) :145-154

[5] Exact flow of a third grade fluid past a porous plate using homotopy analysis method [J].

Ayub, M ;

Rasheed, A ;

Hayat, T .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2003, 41 (18) :2091-2103

[6] Solving systems of ODEs by homotopy analysis method [J].

Bataineh, A. Sami ;

Noorani, M. S. M. ;

Hashim, I. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (10) :2060-2070

[7] Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method [J].

Bataineh, A. Sami ;

Noorani, M. S. M. ;

Hashim, I. .

PHYSICS LETTERS A, 2007, 371 (1-2) :72-82

[8]

Chandrasekhar S., 1938, An Introduction to the Study of Stellar Structure

[9] Series solutions of nano boundary layer flows by means of the homotopy analysis method [J].

Cheng, Jun ;

Liao, Shijun ;

Mohapatra, R. N. ;

Vajraveju, K. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (01) :233-245

[10] Solutions of time-dependent Emden-Fowler type equations by homotopy-perturbation method [J].

Chowdhury, M. S. H. ;

Hashim, I. .

PHYSICS LETTERS A, 2007, 368 (3-4) :305-313

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