(06/02/2012 arXiv:1202.1166, SIAM J. Numer. Anal. 51-4 (2013), pp. 1875-1899)
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in
the numerical treatment of differential systems governed by stiff
and non-stiff terms. This paper discusses order conditions and
symplecticity properties of a class of IMEX Runge--Kutta methods
in the context of optimal control problems.
The analysis of the
schemes is based on the continuous optimality system. Using
suitable transformations of the adjoint equation, order conditions
up to order three are proven as well as the relation between
adjoint schemes obtained through different transformations is
investigated. Conditions for the IMEX Runge--Kutta methods to be
symplectic are also derived. A numerical example illustrating the
theoretical properties is presented.Links
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Michael Herty web page
Sonja Steffensen web page