Highly stable multivalue collocation methods

Abstract

Abstract The paper is focused on the development of A-stable collocation based multivalue methods for stiff problems. This methods are dense output extensions of discrete multivalue methods, since the solution is approximated by a piecewise collocation polynomial with high global regularity. The underlying multivalue method is assumed to be diagonally implicit and with uniform order of convergence, thus it does not suffer from order reduction, as it happens for classical one-step collocation methods. The effectiveness of the approach is also confirmed by the numerical evidence.