Regularity properties of multistage integration methods (Q1379698)

This paper examines the regularity properties of certain classes of diagonally implicit multivalue methods. A method is said to be regular if it has the same set of finite asymptotic values as the underlying differential system. A sufficient condition for regularity is given and this condition is shown to be necessary for all two-step, two-stage methods of order two or more. It is also shown that there exist regular explicit methods.