A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations
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A high-order full-discretization method (FDM) using Hermite interpolation (HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.
KeywordsFull-discretization method Time delay Stability Chatter
This project was partially supported by a scholarship from the China Scholarship Council while Y.L. was visiting the University of Stuttgart. A.F. and P.E. would like to thank the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310) at the University of Stuttgart.
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