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Journal of Applied Mathematics
Volume 2013, Article ID 497863, 13 pages
Research Article

A Third-Order -Laplacian Boundary Value Problem Solved by an SL Lie-Group Shooting Method

Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

Received 3 November 2012; Accepted 18 February 2013

Academic Editor: Ch Tsitouras

Copyright © 2013 Chein-Shan Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The boundary layer problem for power-law fluid can be recast to a third-order -Laplacian boundary value problem (BVP). In this paper, we transform the third-order -Laplacian into a new system which exhibits a Lie-symmetry SL . Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of . The present SL Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order -Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4) method to obtain a quite accurate numerical solution of the -Laplacian.