Stability properties of non-rationally stabilized collocation schemes for stiff boundary value problems

Abstract

This paper deals with a class of perturbed collocation schemes for stiff boundary value problems in systems of first-order ordinary differential equations. To achieve stiff stability for both the decreasing and increasing stiff modes, the perturbation term has to be a non-rational function of the stiffness matrix of the problem. We are mainly concerned with the question of how this function affects the stability function of the scheme, considering in particular stiff stability, A-stability, and global estimates for the stability function in the left half-plane.