STABILITY PROPERTIES OF SOME BOUNDARY-VALUE METHODS

The boundary value methods (BVMs) are a class of numerical methods for solving initial value problems for ODEs. So far they did not have a broad diffusion, essentially for the following two reasons: their stability properties were not clearly understood and, moreover, they were considered too expensive. In this paper we shall analyze the stability properties of three particular BVMs when used for solving linear systems of ODEs. An efficient implementation of these methods will be described in a companion paper [6].