Liao, ShiJun A challenging nonlinear problem for numerical techniques. (English) Zbl 1071.65112 J. Comput. Appl. Math. 181, No. 2, 467-472 (2005). Summary: We show that a nonlinear boundary-value problem describing Blasius viscous flow of a kind of non-Newtonian fluid has an infinite number of explicit analytic solutions. These solutions are rather sensitive to the second-order derivative at the boundary, and the difference of the second derivatives of two obviously different solutions might be less than \(10^{-1000}\). Therefore, it seems impossible to find out all of these solutions by means of current numerical methods. Thus, this nonlinear problem might become a challenge to current numerical techniques. Cited in 11 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 76A05 Non-Newtonian fluids 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Multiple solution; Nonlinear boundary-value problem; boundary layer equation; numerical examples; Sensitivity to boundary conditions; Blasius viscous flow; non-Newtonian fluid PDF BibTeX XML Cite \textit{S. Liao}, J. Comput. Appl. Math. 181, No. 2, 467--472 (2005; Zbl 1071.65112) Full Text: DOI OpenURL References: [1] Schowalter, W.R., The application of boundary-layer theory to power-law pseudo-plastic fluidssimilar solutions, A.i.ch.e. j., 6, 24-28, (1960) [2] Lee, S.Y.; Ames, W.F., Similarity solutions for non-Newtonian fluids, A.i.ch.e. j., 12, 700-708, (1966) [3] Lin, F.N.; Chern, S.Y., Laminar boundary-layer flow of non-Newtonian fluid, Internat. J. heat mass transfer, 22, 1323-1329, (1979) · Zbl 0421.76005 [4] Kim, H.W.; Jeng, D.R.; DeWitt, K.J., Momentum and heat transfer in power-law fluid flow over two-dimensional or axisymmetrical bodies, Internat. J. heat mass transfer, 26, 245-259, (1983) · Zbl 0515.76013 [5] Akçay, M.; Yükselen, M.A., Drag reduction of a non-Newtonian fluid by fluid injection on a moving wall, Arch. appl. mech., 69, 215-225, (1999) · Zbl 0933.76004 [6] Teipel, I., Discontinuities in boundary layer problems of power law fluids, Mech. res. comm., 1, 269-273, (1974) · Zbl 0346.76028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.