Vol.7, No.3, 2008, pp.139-154, doi:10.3970/cmc.2008.007.139
OPEN ACCESS
ARTICLE
The Lie-Group Shooting Method for Solving Classical Blasius Flat-Plate Problem
• Chih-Wen Chang1, Jiang-Ren Chang1, Chein-Shan Liu2
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan. Corresponding author, Tel.: +886-2-24622192x6031. E-mail address: cjr@mail.ntou.edu.tw
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan; Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Abstract
In this paper, we propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf G(T) and the formation of a generalized mid-point Lie group element$\mathbf G(r). Then, by imposing G(T) = G(r) we can derive some algebraic equations to recover the missing initial conditions. It is the first time that we can apply the Lie-group shooting method to solve the classical Blasius flat-plate problem. Numerical examples are worked out to persuade that the novel approach has better efficiency and accuracy with a fast convergence speed by searching a suitable r ∈(0, 1) with the minimum norm to fit the targets.
Keywords
One-step group preserving scheme, Blasius equation, Boundary value problem, Shooting method, Estimation of missing initial condition