In the present paper we consider the second-order boundary-value problem g″ = 1/qūgq, 0<ū<1, (1) with q<0. We search for a positive solution of (1) which satisfies the boundary conditions g′(0) = g(1) = 0. This problem arises in the boundary-layer theory for non-Newtonian fluids. In order to obtain numerical solutions, we use two different iterative methods and a finite-difference scheme. A variable substitution is used in order to improve the approximation and the convergence is accelerated by means of extrapolation methods. Numerical results for different values of q are given and compared with the results obtained by other authors.
Lima, P. M., & Carpentier, M. (2000). Numerical solution of a singular boundary-value problem in non-Newtonian fluid mechanics. Computer Physics Communications, 126(1), 114–120. https://doi.org/10.1016/S0010-4655(99)00422-1