Efficiently implementable multivalue methods for solving stiff ordinary differential equations

Abstract

Although there are now in existence many different types of codes solving stiff ordinary differential equations, the methods upon which these codes are based are often deficient in terms of stability or order criteria. In this paper we discuss some new research on the study of the order, stability and efficiency properties of a general class of methods called multivalue methods. New families of methods based on the extension of diagonally implicitness and singly implicitness from Runge-Kutta methods to multivalue methods are analyzed and a family of methods designed to be implemented in a variable-order variable-stepsize setting is proposed.