Iterative methods for a singular boundary-value problem

We consider a second-order nonlinear ordinary differential equation of the formy″=1qxyq, 0⩽x<1where q<0, with the boundary conditionsy′(0)=y(1)=0.This problem arises in boundary layer equations for the flow of a power-law fluid over an impermeable, semi-infinite flat plane. We show that classical iterative schemes, such as the Picard and Newton methods, converge to the solution of this problem, in spite of the singularity of the solution, if we choose an adequate initial approximation. Moreover, we observe that these methods are more efficient than the methods used before and may be applied to a larger range of values of q. Numerical results for different values of q are given and compared with the results obtained by other authors.