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Numerische Mathematik

, Volume 52, Issue 6, pp 621–638 | Cite as

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

  • Jürgen Bruder
  • Karl Strehmel
  • Rüdiger Weiner
Article

Summary

For the numerical solution of initial value problems of ordinary differential equations partitioned adaptive Runge-Kutta methods are studied. These methods consist of an adaptive Runge-Kutta methods for the treatment of a stiff system and a corresponding explicit Runge-Kutta method for a nonstiff system. First we modify the theory of Butcher series for partitioned adaptive Runge-Kutta methods. We show that for any explicit Runge-Kutta method there exists a translation invariant partitoned adaptive Runge-Kutta method of the same order. Secondly we derive a special translaton invariant partitioned adaptive Runge-Kutta method of order 3. An automatic stiffness detection and a stepsize control basing on Richardson-extrapolation are performed. Extensive tests and comparisons with the partitioned RKF4RW-algorithm from Rentrop [16] and the partitioned algorithm LSODA from Hindmarsh [9] and Petzold [15] show that the partitoned adaptive Runge-Kutta algorithm works reliable and gives good numericals results. Furthermore these tests show that the automatic stiffness detection in this algorithm is effective.

Subject Classifications

AMS(MOS): 65L05 CR: G1.7 

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Jürgen Bruder
    • 1
  • Karl Strehmel
    • 1
  • Rüdiger Weiner
    • 1
  1. 1.Sektion MathematikUniversität HalleHalleGerman Democratic Republic

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