Numerical Algorithms

, Volume 63, Issue 4, pp 679–689 | Cite as

Butcher algebras for Butcher systems

  • Sergey Khashin
Original Paper


We investigate rigorously the properties of the Butcher upper and lower algebras introduced earlier. This investigation provides a new representation of the order conditions which leads to a new approach to simplifying conditions and a way to obtain new methods of high orders explicitly.


Runge-Kutta Butcher system Butcher equations Butcher algebra Algebraic approach to Runge-Kutta 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsIvanovo State UniversityIvanovoRussia

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