A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method
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 lin...
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/497863 |
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| author | Chein-Shan Liu |
| author_facet | Chein-Shan Liu |
| author_sort | Chein-Shan Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-044d88dff3e841b7a19345736ffab4e4 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-044d88dff3e841b7a19345736ffab4e42025-08-20T02:03:07ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/497863497863A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting MethodChein-Shan Liu0Department of Civil Engineering, National Taiwan University, Taipei, TaiwanThe 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.http://dx.doi.org/10.1155/2013/497863 |
| spellingShingle | Chein-Shan Liu A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method Journal of Applied Mathematics |
| title | A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method |
| title_full | A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method |
| title_fullStr | A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method |
| title_full_unstemmed | A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method |
| title_short | A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ) Lie-Group Shooting Method |
| title_sort | third order p laplacian boundary value problem solved by an sl 3 r lie group shooting method |
| url | http://dx.doi.org/10.1155/2013/497863 |
| work_keys_str_mv | AT cheinshanliu athirdorderplaplacianboundaryvalueproblemsolvedbyansl3rliegroupshootingmethod AT cheinshanliu thirdorderplaplacianboundaryvalueproblemsolvedbyansl3rliegroupshootingmethod |