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**A challenging nonlinear problem for numerical techniques.**
*(English)*
Zbl 1071.65112

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.

### 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
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\textit{S. Liao}, J. Comput. Appl. Math. 181, No. 2, 467--472 (2005; Zbl 1071.65112)

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### References:

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