Modelling and simulation of autonomous oscillators with random parameters

Roland Pulch

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 6, 1128-1143

Abstract: We consider periodic problems of autonomous systems of ordinary differential equations or differential algebraic equations. To quantify uncertainties of physical parameters, we introduce random variables in the systems. Phase conditions are required to compute the resulting periodic random process. It follows that the variance of the process depends on the choice of the phase condition. We derive a necessary condition for a random process with a minimal total variance by the calculus of variations. A corresponding numerical method is constructed based on the generalised polynomial chaos. We present numerical simulations of two test examples.

Keywords: Ordinary differential equation; Differential algebraic equation; Uncertainty quantification; Polynomial chaos; Calculus of variations (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:6:p:1128-1143

DOI: 10.1016/j.matcom.2010.10.028

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