Numerical solution of a singular boundary-value problem in non-Newtonian fluid mechanics
In the present paper we consider the second-order boundary-value problem g " = 1/q (u) over bar g(q), 0 < (u) over bar < 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. (C) 2000 Elsevier Science B.V. All rights reserved.
finite-difference scheme extrapolation methods nonlinear boundary-value problem picard method newton method subsolution supersolution