Analytical and numerical results for the Swift-Hohenberg equation

F. Talay Akyildiz, Dennis A. Siginer, K. Vajravelu, Robert A. Van Gorder

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)221-226
Number of pages6
JournalApplied Mathematics and Computation
Issue number1
Publication statusPublished - Mar 1 2010

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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