A challenging nonlinear problem for numerical techniques

作者:

Highlights:

摘要

In this paper 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.

论文关键词:34B15,68Q17,65L12,65L17,Multiple solution,Nonlinearity,Sensitivity to boundary conditions

论文评审过程:Received 7 July 2004, Revised 15 November 2004, Available online 20 January 2005.

论文官网地址:https://doi.org/10.1016/j.cam.2004.11.039