Order Properties of Implicit Multivalue Methods for Ordinary Differential Equations

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Abstract
The family of multivalue methods, which may be used in the numerical solution of ordinary differential equations, is a very general one, containing as particular members such disparate methods as linear multistep, Runge-Kutta, and hybrid methods. In this paper, a characterization of the order properties of multivalue methods is obtained that enables not only a unification of the order theories of many apparently different classes of numerical methods but also the study of the order of many new types of methods. General results concerning the maximum order of multivalue methods are given, and some consideration is given towards the selection of methods suitable for the numerical solution of stiff differential equations.

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