Analytical and numerical results for the Swift-Hohenberg equation

    Authors

    F. T. Akyildiz; D. A. Siginer; K. Vajravelu;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Swift-Hohenberg equation; Fisher-Kolmogorov equation; Higher order; parabolic model equations; Series solution; Convergent solution; PROPAGATING FRONTS; STRETCHING PLATE; FLOWS; FLUID; Mathematics, Applied

    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.

    Journal Title

    Applied Mathematics and Computation

    Volume

    216

    Issue/Number

    1

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    221

    Last Page

    226

    WOS Identifier

    WOS:000274719600023

    ISSN

    0096-3003

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