Homotopy analysis method for singular IVPs of Emden-Fowler type

Research output: Contribution to journalArticle

88 Citations (Scopus)

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 languageEnglish
Pages (from-to)1121-1131
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number4
DOIs
Publication statusPublished - Apr 2009

Fingerprint

Homotopy Analysis Method
Singular Problems
Initial value problems
Initial Value Problem
Homotopy Perturbation Method
Adomian Decomposition Method
Second-order Ordinary Differential Equations
Series Solution
Analytical Solution
Ordinary differential equations
Decomposition

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Homotopy analysis method for singular IVPs of Emden-Fowler type. / Bataineh, A. Sami; Md. Noorani, Mohd. Salmi; Hashim, Ishak.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, 04.2009, p. 1121-1131.

Research output: Contribution to journalArticle

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