Stability Function of Implicit RK-Methods

Abstract

Methods are called A -stable if there are no stability restrictionsfor y ′ = λy, Re λ < 0 and h > 0. This concept was introducedby Dahlquist (1963) for linear multistep methods, but also appliedto Runge-Kutta processes. Ehle (1968) and Axelsson (1969) then independentlyinvestigated the A -stability of implicit Runge-Kutta methods andproposed new classes of A -stable methods. A nice paper of Wright(1970) studied collocation methods.