Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013 (2013), Article ID 497863, 13 pages.
A Third-Order -Laplacian Boundary Value Problem Solved by an SL Lie-Group Shooting Method
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.
J. Appl. Math., Volume 2013 (2013), Article ID 497863, 13 pages.
First available in Project Euclid: 14 March 2014
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Liu, Chein-Shan. A Third-Order $p$ -Laplacian Boundary Value Problem Solved by an SL $\left(3,ℝ\right)$ Lie-Group Shooting Method. J. Appl. Math. 2013 (2013), Article ID 497863, 13 pages. doi:10.1155/2013/497863. https://projecteuclid.org/euclid.jam/1394807916