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

Chein-Shan Liu

Journal of Applied Mathematics, 2013, vol. 2013, 1-13

Abstract:

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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/JAM/2013/497863.pdf (application/pdf)
http://downloads.hindawi.com/journals/JAM/2013/497863.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:497863

DOI: 10.1155/2013/497863

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().