| Source | CMC, Vol. 7, No. 3, pp. 139-154 |
| Download | Full length paper in PDF format. Size = 312,976 bytes |
| Keywords | One-step group preserving scheme, Blasius equation, Boundary value problem, Shooting method, Estimation of missing initial condition |
| 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 $\mathbf {G}(T) = \mathbf {G}(r)$ 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 $r \in (0,\tmspace +\thickmuskip {.2777em} 1)$ with the minimum norm to fit the targets. |