Homotopy analysis method for singular IVPs of Emden-Fowler type

A. Sami Bataineh; M. S.M. Noorani; I. Hashim

doi:10.1016/j.cnsns.2008.02.004

Homotopy analysis method for singular IVPs of Emden-Fowler type

A. Sami Bataineh
, M. S.M. Noorani
, I. Hashim

Universiti Kebangsaan Malaysia

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1121-1131
Number of pages	11
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	14
Issue number	4
DOIs	https://doi.org/10.1016/j.cnsns.2008.02.004
State	Published - Apr 2009
Externally published	Yes

Keywords

Emden-Fowler equations
Homotopy analysis method
Lane-Emden equation
Singular IVPs

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10.1016/j.cnsns.2008.02.004

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title = "Homotopy analysis method for singular IVPs of Emden-Fowler type",

abstract = "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.",

keywords = "Emden-Fowler equations, Homotopy analysis method, Lane-Emden equation, Singular IVPs",

author = "Bataineh, \{A. Sami\} and Noorani, \{M. S.M.\} and I. Hashim",

year = "2009",

month = apr,

doi = "10.1016/j.cnsns.2008.02.004",

language = "English",

volume = "14",

pages = "1121--1131",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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TY - JOUR

T1 - Homotopy analysis method for singular IVPs of Emden-Fowler type

AU - Bataineh, A. Sami

AU - Noorani, M. S.M.

AU - Hashim, I.

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

KW - Emden-Fowler equations

KW - Homotopy analysis method

KW - Lane-Emden equation

KW - Singular IVPs

UR - https://www.scopus.com/pages/publications/55549143019

U2 - 10.1016/j.cnsns.2008.02.004

DO - 10.1016/j.cnsns.2008.02.004

M3 - Article

AN - SCOPUS:55549143019

SN - 1007-5704

VL - 14

SP - 1121

EP - 1131

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 4

ER -

Homotopy analysis method for singular IVPs of Emden-Fowler type

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Keywords

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