Numerische Mathematik

, Volume 36, Issue 4, pp 431–445

Order conditions for numerical methods for partitioned ordinary differential equations

  • E. Hairer

DOI: 10.1007/BF01395956

Cite this article as:
Hairer, E. Numer. Math. (1981) 36: 431. doi:10.1007/BF01395956


Motivated by the consideration of Runge-Kutta formulas for partitioned systems, the theory of “P-series” is studied. This theory yields the general structure of the order conditions for numerical methods for partitioned systems, and in addition for Nyström methods fory″=f(y,y′), for Rosenbrock-type methods with inexact Jacobian (W-methods). It is a direct generalization of the theory of Butcher series [7, 8]. In a later publication, the theory ofP-series will be used for the derivation of order conditions for Runge-Kutta-type methods for Volterra integral equations [1].

Subject Classifications

AMS(MOS): 65L05 CR:5.17 

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • E. Hairer
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelberg 1Germany (Fed. Rep.)