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

International Journal for Numerical Methods in Engineering · 2004 · Vol. 61(1) · pp. 117–141

Tamás Insperger✉(Budapest University of Technology and Economics)Gábor Stépàn(Twitter (United States))

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.

Numerical methods for differential equations Electromagnetic Simulation and Numerical Methods Advanced Mathematical Modeling in EngineeringDiscretizationMathematicsStability (learning theory)Convergence (economics)Delay differential equationMathieu functionDiscrete time and continuous timeApplied mathematicsMatrix (chemical analysis)Differential equation

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References

Semi‐discretization method for delayed systems

International Journal for Numerical Methods in Engineering · 2002 · 669 citations

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