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2013 A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,) Lie-Group Shooting Method
Chein-Shan Liu
J. Appl. Math. 2013: 1-13 (2013). DOI: 10.1155/2013/497863

Abstract

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,). 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,) 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.

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Chein-Shan Liu. "A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,) Lie-Group Shooting Method." J. Appl. Math. 2013 1 - 13, 2013. https://doi.org/10.1155/2013/497863

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.35110
MathSciNet: MR3039723
Digital Object Identifier: 10.1155/2013/497863

Rights: Copyright © 2013 Hindawi

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