Analytical and numerical results for the Swift-Hohenberg equation

Journal article

Authors/Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Akyildiz FT, Siginer DA, Vajravelu K, Van Gorder RA

Publisher: Elsevier

Place: NEW YORK

Publication year: 2010

Journal: Applied Mathematics and Computation (0096-3003)

Journal acronym: APPL MATH COMPUT

Volume number: 216

Issue number: 1

Start page: 221

End page: 226

Number of pages: 6

ISSN: 0096-3003

eISSN: 1873-5649

Languages: English-Great Britain (EN-GB)

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Abstract

The problem of the Swift-Hohenberg equation is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed and documented here for the first time. In particular, we focus on the roles of the eigenvalue parameter alpha and the length parameter l on the large time behaviour of the solution. For a given time t, we obtain analytical expressions for eigenvalue parameter alpha and length l which show how different values of these parameters may lead to qualitatively different large time profiles. Also, the results are presented graphically. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress. (C) 2010 Elsevier Inc. All rights reserved.

Keywords

Convergent solution, Fisher-Kolmogorov equation, Higher order parabolic model equations, Series solution, Swift-Hohenberg equation

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