Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Abstract

The spectral element method was introduced by Khasawneh and Mann (2013) for the stability analysis of time-periodic delay-differential equations (DDEs) with multiple delays. In this paper, this method is generalized for time-periodic DDEs with multiple delays and distributed delay. For this general case, an explicit formula is given for the construction of the matrix approximation of the monodromy operator. The derived formula enables the algorithmic application of the method to DDEs with general combinations of delays for arbitrary point sets and test functions. Stability analysis is demonstrated for specific case studies, and the computation code is provided for a complex example.