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 b road diffusion, essentially for the following two reasons: their stabi lity properties were not clearly understood and, moreover, they were c onsidered too expensive. In this paper we shall analyze the stability properties of three particular BVMs when used for solving linear syste ms of ODEs. An efficient implementation of these methods will be descr ibed in a companion paper [6].