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
Copyright Status
Unknown
Socpus ID
77049099287 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/77049099287
STARS Citation
Talay Akyildiz, F.; Siginer, Dennis A.; Vajravelu, K.; and Van Gorder, Robert A., "Analytical And Numerical Results For The Swift-Hohenberg Equation" (2010). Scopus Export 2010-2014. 1286.
https://stars.library.ucf.edu/scopus2010/1286