Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

2004/07/21 by Tamás Insperger, Gábor Stépàn, Gábor Stépán · 16 citations
Mathematics · Engineering · Computer Science · #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods #Advanced Mathematical Modeling in Engineering

paper · doi:10.1002/nme.1061

Abstract

Abstract An updated version of the semi‐discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time‐period/time‐delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.

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