Stability Function of Implicit RK-Methods

  • Ernst Hairer
  • Gerhard Wanner
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 14)

Abstract

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Ernst Hairer
    • 1
  • Gerhard Wanner
    • 1
  1. 1.Section de Mathématiques, C.P. 240Université de GenèveGenève 24Switzerland

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