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Passive Integration Methods: Fundamental Theory

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Abstract:

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.

Keywords: Duffing's equation; Passive integration; Runge-Kutta methods; Wave digital structures

Document Type: Original Article

DOI: https://doi.org/10.1078/14348410122267348

Affiliations: Department of Electrical Engineering and Information Technology/Communications Theory, University of Paderborn, D-33095 Paderborn, Germany. E-mail: ochs@ieee.org

Publication date: 2001-05-01

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