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Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions

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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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Authors and Affiliations

  1. Department of Electrical Engineering & Information Technology, University of Paderborn, 33095, Paderborn, Germany

    D. Fränken

  2. Department of Electrical Engineering & Information Technology, Ruhr-University, 44780, Bochum, Germany

    K. Ochs

Authors
  1. D. Fränken
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  2. K. Ochs
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Fränken, D., Ochs, K. Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions. BIT Numerical Mathematics 43, 339–361 (2003). https://doi.org/10.1023/A:1026039820006

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