Modified homotopy analysis method for solving systems of second-order BVPs

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Abstract

In this paper, a new modification of the homotopy analysis method (HAM) is presented for solving systems of second-order boundary-value problems (BVPs). The main advantage of the modified HAM (MHAM) is that one can avoid the uncontrollability problems of the nonzero endpoint conditions encountered in the standard HAM. Numerical comparisons show that the MHAM is more efficient than the standard HAM.

Original languageEnglish
Pages (from-to)430-442
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number2
DOIs
Publication statusPublished - Feb 2009

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Homotopy Analysis Method
boundary value problems
Boundary value problems
Boundary Value Problem
Numerical Comparisons
Standards

Keywords

  • Boundary-value problems
  • Homotopy analysis method
  • Modified homotopy analysis method

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

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title = "Modified homotopy analysis method for solving systems of second-order BVPs",
abstract = "In this paper, a new modification of the homotopy analysis method (HAM) is presented for solving systems of second-order boundary-value problems (BVPs). The main advantage of the modified HAM (MHAM) is that one can avoid the uncontrollability problems of the nonzero endpoint conditions encountered in the standard HAM. Numerical comparisons show that the MHAM is more efficient than the standard HAM.",
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AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

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AB - In this paper, a new modification of the homotopy analysis method (HAM) is presented for solving systems of second-order boundary-value problems (BVPs). The main advantage of the modified HAM (MHAM) is that one can avoid the uncontrollability problems of the nonzero endpoint conditions encountered in the standard HAM. Numerical comparisons show that the MHAM is more efficient than the standard HAM.

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