Approximate analytical solutions of systems of PDEs by homotopy analysis method

Research output: Contribution to journalArticle

43 Citations (Scopus)

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 languageEnglish
Pages (from-to)2913-2923
Number of pages11
JournalComputers and Mathematics with Applications
Volume55
Issue number12
DOIs
Publication statusPublished - Jun 2008

Fingerprint

Homotopy Analysis Method
Systems of Partial Differential Equations
Partial differential equations
Analytical Solution
Series Solution
Variational Iteration Method
Second order differential equation
Partial differential equation
Nonlinear Systems
Linear Systems
First-order
Linear systems
Nonlinear systems

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Approximate analytical solutions of systems of PDEs by homotopy analysis method. / Sami Bataineh, A.; Md. Noorani, Mohd. Salmi; Hashim, Ishak.

In: Computers and Mathematics with Applications, Vol. 55, No. 12, 06.2008, p. 2913-2923.

Research output: Contribution to journalArticle

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