Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method

摘要

The Chow-Yorke algorithm is a homotopy method that has been proved globally convergent for Brouwer fixed-point problems, certain classes of zero finding and nonlinear programming problems, and two-point boundary-value approximations based on shooting and finite differences. The method is numerically stable and has been successfully applied to a wide range of practical engineering problems. Here the Chow-Yorke algorithm is proved globally convergent for a class of spline-collocation approximations to nonlinear two-point boundary-value problems. Several numerical implementations of the algorithm are briefly described, and computational results are presented for a fairly difficult fluid-dynamics boundary-value problem.