Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions |
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| Authors: | D Fränken K Ochs |
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| Institution: | (1) Department of Electrical Engineering & Information Technology, University of Paderborn, 33095 Paderborn, Germany;(2) Department of Electrical Engineering & Information Technology, Ruhr-University, 44780 Bochum, Germany |
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| Abstract: | In this paper, a new class of Runge–Kutta methods is introduced. Some basic properties of this subgroup of algebraically stable methods are presented and a complete parametric representation is given. Necessary and sufficient order conditions for lower order methods as well as sufficient order conditions for higher order methods are derived yielding a significantly reduced number of conditions when compared with general Runge–Kutta methods. Design examples conclude this paper. |
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| Keywords: | Runge– Kutta methods passivity losslessness algebraic stability parametric representation trees order conditions simplifying assumptions |
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