A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

作者：Liu, Yilong^*; Fischer, Achim; Eberhard, Peter; Wu, Baohai

来源：Acta Mechanica Sinica, 2015, 31(3): 406-415.

DOI：10.1007/s10409-015-0397-6

• Full-discretization method
• Time delay
• Stability
• Chatter

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.

• 出版日期2015-6
• 单位西北工业大学