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Numerische Mathematik

, Volume 58, Issue 1, pp 243–254 | Cite as

Equilibria of Runge-Kutta methods

  • E. Hairer
  • A. Iserles
  • J. M. Sanz-Serna
Article

Summary

It is known that certain Runge-Kutta methods share the property that, in a constant-step implementation, if a solution trajectory converges to a bounded limit then it must be a fixed point of the underlying differential system. Such methods are calledregular. In the present paper we provide a recursive test to check whether given method is regular. Moreover, by examining solution trajectories of linear equations, we prove that the order of ans-stage regular method may not exceed 2[(s+2)/2] and that the maximal order of regular Runge-Kutta method with an irreducible stability function is 4.

Subject classifications

AMS(MOS): 65L05 CR: G1.7 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • E. Hairer
    • 1
  • A. Iserles
    • 2
  • J. M. Sanz-Serna
    • 3
  1. 1.Section de MathématiquesUniversité de GenèveSwitzerland
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeUK
  3. 3.Departamento de Matemática Aplicada y Computación, Facultad de CienciasUniversidad de ValladolidSpain

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