Solutions of heat-like and wave-like equations with variable coefficients by means of the homotopy analysis method

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Abstract

We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter Latin small letter h with stroke, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.

Original languageEnglish
Pages (from-to)589-592
Number of pages4
JournalChinese Physics Letters
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Feb 2008

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heat of solution
wave equations
heat
coefficients
strokes
boundary value problems
iteration
decomposition

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter Latin small letter h with stroke, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.",
author = "Alomari, {A. K.} and {Md. Noorani}, {Mohd. Salmi} and {Mohd. Nazar}, Roslinda",
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AU - Alomari, A. K.

AU - Md. Noorani, Mohd. Salmi

AU - Mohd. Nazar, Roslinda

PY - 2008/2/1

Y1 - 2008/2/1

N2 - We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter Latin small letter h with stroke, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.

AB - We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter Latin small letter h with stroke, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.

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