Implementation of Implicit Runge-Kutta Methods

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

Abstract

If the dimension of the differential equation y′ = f(x, y) is n, then the s -stage fully implicit Runge-Kutta method (3.1) involves a n · s -dimensional nonlinear system for the unknowns g 1, ... , g s . An efficient solution of this system is the main problem in the implementation of an implicit Runge-Kutta method.

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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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