Feasibility and contractivity in implicit Runge-Kutta methods

摘要

This paper is concerned with implicit Runge-Kutta methods for the numerical solution of initial value problems in ordinary differential equations. For these methods a review is presented of the fundamental concept of algebraic stability (introduced in 1979 independently by Burrage, Butcher and by Crouzeix). Furthermore, a new framework is given in which algebraic stability becomes equivalent to both contractivity and feasibility of a Runge-Kutta method.