W. Oevel, M. Sofroniou
Modified Order Theory for Partitioned Runge-Kutta and Runge-Kutta-Nyström Methods

MSC:

65L05 Initial value problems

70H05 Hamilton's equations

Abstract: A parametrization technique for deriving general symplectic and/or self-
adjoint (symmetric) Runge-Kutta methods of standard type was discussed in a recent
paper by the authors. Here these results are extended to the derivation of order condi-
tions for partitioned and Nyström-Runge-Kutta methods. These methods are of pertic-
ular interest for the symplectic time-integration of Hamiltonian systems in separable form.
Keywords: partitioned Runge-Kutta methods, Runge-Kutta-Nyström methods, symplectic, symmetric, self-adjoint, symplectic integration