Adaptive Methods for Piecewise Polynomial Collocation for Ordinary Differential Equations (2003)

Author(s): Wright, K.

Abstact: Various adaptive algorithms for the solution of ordinary differential boundary value problems using piecewise polynomial collocation are considered. Five different criteria are compared using both interval subdivision and mesh redistribution. All the algorithms are based on the idea of equidistribution of a criterion. It is, however, shown that when accuracy is poor that equidistribution may not give a unique solution. The main results indicate that mesh redistribution is more reliable than interval subdivision, and give an evaluation of the five criteria.