Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

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

doi:10.1016/j.physleta.2007.05.094

Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

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

Universiti Kebangsaan Malaysia

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

98 Scopus citations

Abstract

In this Letter, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of 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)	72-82
Number of pages	11
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	371
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physleta.2007.05.094
State	Published - 5 Nov 2007
Externally published	Yes

Keywords

Homotopy analysis method
Time-dependent Emden-Fowler equation
Time-dependent Lane-Emden equation
Wave-type equation

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10.1016/j.physleta.2007.05.094

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title = "Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method",

abstract = "In this Letter, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of 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 = "Homotopy analysis method, Time-dependent Emden-Fowler equation, Time-dependent Lane-Emden equation, Wave-type equation",

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

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T1 - Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

AU - Sami Bataineh, A.

AU - Noorani, M. S.M.

AU - Hashim, I.

PY - 2007/11/5

Y1 - 2007/11/5

N2 - In this Letter, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of 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 Letter, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of 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 - Homotopy analysis method

KW - Time-dependent Emden-Fowler equation

KW - Time-dependent Lane-Emden equation

KW - Wave-type equation

UR - https://www.scopus.com/pages/publications/35348973440

U2 - 10.1016/j.physleta.2007.05.094

DO - 10.1016/j.physleta.2007.05.094

M3 - Article

AN - SCOPUS:35348973440

SN - 0375-9601

VL - 371

SP - 72

EP - 82

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -

Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

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Keywords

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