Proceedings of the 5th International Conference on Advanced Design and Manufacturing Engineering

A simple time domain collocation method for solving the van der Pol oscillator

Fei Han, Ming Li, Shijie Zhang
Corresponding author
Fei Han
Time domain collocation method; high dimensional harmonic balance method; period solution; van der Pol equation; limit cycle.
In this paper, the time domain collocation method (TDC) is applied to solve the van der Pol equation. The results obtained by the TDC are compared with the results by the traditional harmonic balance method (HB) and high dimensional harmonic balance method (HDHB). For the extended TDC method, appropriately increasing the number of collocation points can significantly relive the nonphysical solution phenomenon and generate a better solution. Compared with the HDHB, the TDC method is derived more strictly, and more convenient to implement. Numerical results verify the simplicity, accuracy and efficiency of the present TDC method.
Download article (PDF)