Iterative methods for a singular boundary-value problem

✍ Scribed by P.M. Lima; M.P. Carpentier

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 131 KB
• Volume: 111
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00141-7

✦ Synopsis

We consider a second-order nonlinear ordinary di erential equation of the form y = 1 q xy q ; 06x ¡ 1 where q ¡ 0, with the boundary conditions

This problem arises in boundary layer equations for the ow of a power-law uid over an impermeable, semi-inÿnite at 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 e cient than the methods used before and may be applied to a larger range of values of q.

Numerical results for di erent values of q are given and compared with the results obtained by other authors.