TY - EJOU AU - Liu, Chein-Shan AU - Chang, Chih-Wen AU - Chang, Jiang-Ren TI - A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics T2 - Computer Modeling in Engineering \& Sciences PY - 2008 VL - 32 IS - 1 SN - 1526-1506 AB - In this paper, we propose a new method to tackle of two famous boundary layer equations in fluid mechanics, namely, the Falkner-Skan and the Blasius equations. We can employ this method 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$\mathbf {G}(T) = \mathbf {G}(r)$ we can seek the missing initial conditions through a minimum discrepancy from the target in terms of a weighting factor$r \in (0, 1)$. Numerical examples are worked out to persuade that this novel approach has good efficiency and accuracy with a fast convergence speed by searching$r$ with the minimum norm to fit two targets. KW - One-step group preserving scheme KW - Falkner-Skan equation KW - Blasius equation KW - Boundary value problem KW - Lie-group shooting method KW - Estimation of missing initial condition DO - 10.3970/cmes.2008.032.001