Runge-Kutta methods for affinely controlled nonlinear systems

Authors:
Peter E. Kloeden;Andreas Röíler
Affiliations:
Johann Wolfgang Goethe Universität, Fachbereich Mathematik, D-60054 Frankfurt am Main, Germany;Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge-Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grune and Kloeden.