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

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  • Chein-Shan Liu

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.

Suggested Citation

  • Chein-Shan Liu, 2013. "A Third-Order -Laplacian Boundary Value Problem Solved by an SL Lie-Group Shooting Method," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-13, March.
    • Handle: RePEc:hin:jnljam:497863
    DOI: 10.1155/2013/497863
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