Title

Analytical And Numerical Results For The Swift-Hohenberg Equation

Keywords

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

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 α 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 α 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. © 2010 Elsevier Inc. All rights reserved.

Publication Date

3-1-2010

Publication Title

Applied Mathematics and Computation

Volume

216

Issue

1

Number of Pages

221-226

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.amc.2010.01.041

Socpus ID

77049099287 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/77049099287

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