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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

journal of applied mathematics

A Third-Order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-Laplacian Boundary Value Problem Solved by an SL<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi>ℝ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>Lie-Group Shooting Method

A Third-Orderp-Laplacian Boundary Value Problem Solved by an SL(3,ℝ)Lie-Group Shooting Method