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

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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 languageEnglish
Pages (from-to)72-82
Number of pages11
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume371
Issue number1-2
DOIs
Publication statusPublished - 5 Nov 2007

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decomposition
perturbation

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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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 {Md. Noorani}, {Mohd. Salmi} and Ishak Hashim",
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T1 - Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

AU - Sami Bataineh, A.

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

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

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

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

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