Solving Galerkin Approximations to Nonlinear Two-Point Boundary Value Problems by a Globally Convergent Homotopy Method

Watson, Layne T. and Scott, L. Ridgway (1986) Solving Galerkin Approximations to Nonlinear Two-Point Boundary Value Problems by a Globally Convergent Homotopy Method. Technical Report TR-86-27, Computer Science, Virginia Polytechnic Institute and State University.

Abstract

The Chow-Yorke algorithm, i.e., a homotopy method that has been proved globally convergent j problems, certain classes of zero finding and nonlinear programming problems, and two-point, boundary based on shooting, finite differences, and spline collocation. The method is numerically stable and has been applied to a wide range of practical engineering problems. Here the Chow-Yorke algorithm is proved globally c Galerkin approximations to nonlinear two-point boundary value problems. Several numerical implement are briefly described, and computational results are presented for a fairly difficult, magnet-hydrodynamic problem. Key words. homotopy method, Chow-Yorke algorithm, globally convergent,, two-point boundary value method, finite element method, nonlinear equations