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Passive integration methods: Fundamental theory
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DOI：10.1078/1434-8411-00024.png)
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Methods based on the wave digital concept are suited for the modelling of passive physical systems. The generated wave digital models inhere both a high physical transparency as well as a variety of good numerical properties. However, the wave digital concept is known for linear multistep methods only. In this context, passivity imposes a limited accuracy. To this end, more universal integration methods are considered in this paper: The so-called general linear methods which cover in particular linear multistep methods and RUNGE-KUTTA methods. In order to establish a new theory for these integration methods, a network theoretical approach is used. A new class of RUNGE-KUTTA methods will be derived. The generated algorithmic models inhere the same good properties as wave digital models but their numerical accuracy is increased. A simulation example for a nonlinear physical system will be given.
Keyword:
passive integration
RUNGE-KUTTA methods
wave digital structures
Duffing's equation
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