Improving the computational efficiency and accuracy of the semi-discretization method for periodic delay-differential equations

When analyzing the computational efficiency of the semi-discretization method for periodic delay-differential equations, the computation of the transition matrix of the approximated system is identified to cause most of the computational cost. Different measures to increase computational efficiency of the semi-discretization method are proposed. For systems with piecewise defined delay terms as they occur, e.g., in interrupted cutting processes, a predefined non-equidistant discretization scheme is introduced which significantly reduces computational cost and, at the same time, increases accuracy of the method. The proposed measures are demonstrated by means of a 2-dof milling process.