Approximate analytical solutions of systems of PDEs by homotopy analysis method

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

doi:10.1016/j.camwa.2007.11.022

Approximate analytical solutions of systems of PDEs by homotopy analysis method

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

Universiti Kebangsaan Malaysia

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

67 Scopus citations

Abstract

In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

Original language	English
Pages (from-to)	2913-2923
Number of pages	11
Journal	Computers and Mathematics with Applications
Volume	55
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2007.11.022
State	Published - Jun 2008
Externally published	Yes

Keywords

Adomian decomposition method
Homotopy analysis method
Nonlinear systems
Systems of PDEs
Variational iteration method

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10.1016/j.camwa.2007.11.022

Cite this

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title = "Approximate analytical solutions of systems of PDEs by homotopy analysis method",

abstract = "In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.",

keywords = "Adomian decomposition method, Homotopy analysis method, Nonlinear systems, Systems of PDEs, Variational iteration method",

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year = "2008",

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T1 - Approximate analytical solutions of systems of PDEs by homotopy analysis method

AU - Sami Bataineh, A.

AU - Noorani, M. S.M.

AU - Hashim, I.

PY - 2008/6

Y1 - 2008/6

N2 - In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

AB - In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

KW - Adomian decomposition method

KW - Homotopy analysis method

KW - Nonlinear systems

KW - Systems of PDEs

KW - Variational iteration method

UR - https://www.scopus.com/pages/publications/42749084915

U2 - 10.1016/j.camwa.2007.11.022

DO - 10.1016/j.camwa.2007.11.022

M3 - Article

AN - SCOPUS:42749084915

SN - 0898-1221

VL - 55

SP - 2913

EP - 2923

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Approximate analytical solutions of systems of PDEs by homotopy analysis method

Abstract

Keywords

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