SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Implicit-Explicit Runge-Kutta schemes for optimal control problems and applications to PDEs

L. Pareschi

Abstract
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. In this talk we discuss order conditions and symplecticity properties of a class of IMEX Runge-Kutta methods in the context of optimal control problems. 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. Applications to some partial differential equations are finally presented.

Bibliography
[1] M. Herty, L. Pareschi and S. Steffensen, Implicit-Explicit Runge-Kutta schemes for numerical discretization of optimal control problems, SIAM J. Num. Anal. to appear (arXiv: 1202.1166)
[2] G. Albi , M. Herty, C. Jörres and L. Pareschi, Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model, preprint 2013

Organized by         Universidad de Valladolid     IMUVA