TY - JOUR
T1 - Analytical and numerical results for the Swift-Hohenberg equation
AU - Talay Akyildiz, F.
AU - Siginer, Dennis A.
AU - Vajravelu, K.
AU - Van Gorder, Robert A.
PY - 2010/3/1
Y1 - 2010/3/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.amc.2010.01.041
DO - 10.1016/j.amc.2010.01.041
M3 - Article
AN - SCOPUS:77049099287
SN - 0096-3003
VL - 216
SP - 221
EP - 226
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1
ER -