ON A CLASS OF ENCLOSURE METHODS FOR INITIAL-VALUE PROBLEMS

This paper deals with the computation of interval enclosures for the s olutions of initial value problems in systems of ordinary differential equations. We present a particular class of enclosure methods based o n the Taylor series method. They are expressed in a single algorithm c ontaining some parameters which may be chosen arbitrarily. However, a skillful choice is necessary in order to keep the widths of the enclos ing intervals sufficiently small. We give some theoretical results abo ut the behaviour of these widths.