Numerische Mathematik

, Volume 13, Issue 1, pp 14–23 | Cite as

The order of some implicit Runge-Kutta methods

  • J. H. Verner


The orders of some single step methods for the solution of a general system of differential equations are established. Leading error terms are given.


Differential Equation Error Term Mathematical Method General System Single Step 
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  1. 1.
    Butcher, J. C.: Implicit Runge-Kutta processes. Math. Comp.18, 50–64 (1964).Google Scholar
  2. 2.
    —— Integration processes based on Radau quadrature formulas. Math. Comp.18, 233–244 (1964).Google Scholar
  3. 3.
    Cooper, G. J.: A class of single step methods for systems of nonlinear differential equations. Math. Comp.21, 597–610 (1967).Google Scholar
  4. 4.
    —— Interpolation and quadrature methods for ordinary differential equations. Math. Comp.22, 69–76 (1968).Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • J. H. Verner
    • 1
  1. 1.Department of Computer ScienceUniversity of EdinburghEdinburghScotland

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