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A new shooting method for solving boundary layer equations in fluid mechanics. (English) Zbl 1232.65104

Summary: 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 \(\mathbb{G}(T)\) and the formation of a generalized mid-point Lie group element \(\mathbb{G}(r)\). Then, by imposing \(\mathbb{G}(T) = \mathbb{G}(r)\) 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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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