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.
", pages = "153-163", url = "http://www.ingentaconnect.com/content/urban/541/2001/00000055/00000003/art00024", keyword = "Passive integration, Runge-Kutta methods, Wave digital structures, Duffing's equation" }