Simplifying assumptions for the order of partitioned multivalue methods

In solving a system of ordinary differential equations by multivalue methods, the concept of partitioning such a method into two parts corresponding to “internal” and “external” computations has recently been introduced by Burrage and Butcher [3]. In this paper the order conditions for such methods will be given and simplifying assumptions for them derived. Various examples are presented and, in particular, a new class of methods is introduced and its order properties are studied.