Chang, Chih-Wen; Chang, Jiang-Ren; Liu, Chein-Shan The Lie-group shooting method for solving classical Blasius flat-plate problem. (English) Zbl 1231.76082 CMC, Comput. Mater. Continua 7, No. 3, 139-154 (2008). Summary: 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. This is the first time that the Lie-group shooting method has been applied to solve the classical Blasius flat-plate problem. Numerical examples are worked out to show that this novel approach has better efficiency and accuracy, with a fast convergence speed obtained by searching for a suitable \(r\in(0,1)\) with the minimum norm to fit the targets Cited in 4 Documents MSC: 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76M50 Homogenization applied to problems in fluid mechanics Keywords:one-step group preserving scheme; Blasius equation; boundary value problem; shooting method; estimation of missing initial condition PDFBibTeX XMLCite \textit{C.-W. Chang} et al., CMC, Comput. Mater. Continua 7, No. 3, 139--154 (2008; Zbl 1231.76082) Full Text: DOI