Analytical and numerical results for the Swift-Hohenberg equation

作者：Akyildiz F Talay; Siginer Dennis A; Vajravelu K^*; Van Gorder Robert A

来源：Applied Mathematics and Computation, 2010, 216(1): 221-226.

DOI：10.1016/j.amc.2010.01.041

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

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.

• 出版日期2010-3-1