Lie-Butcher theory for Runge-Kutta methods

  title={Lie-Butcher theory for Runge-Kutta methods},
  author={Hans Munthe Kaas},
  • Hans Munthe Kaas
  • Published 1995
Runge{Kutta methods are formulated via coordinate independent operations on manifolds. It is shown that there is an intimate connection between Lie series and Lie groups on one hand and Butcher's celebrated theory of order conditions on the other. In Butcher's theory the elementary di erentials are represented as trees. In the present formulation they appear as commutators between vector elds. This leads to a theory for the order conditions, which can be developed in a completely coordinate… CONTINUE READING
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