A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-28
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP).
In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ).
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 r∈[0,1].
The present SL(3,ℝ) Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-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 p-Laplacian.
American Psychological Association (APA)
Liu, Chein-Shan. 2013. A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-476436
Modern Language Association (MLA)
Liu, Chein-Shan. A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method. Journal of Applied Mathematics No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-476436
American Medical Association (AMA)
Liu, Chein-Shan. A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-476436
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476436