On the higher-order semi-discretizations for periodic delayed systems

Semi-discretization techniques of periodic delayed systems are presented using zeroth-, first- and higher-order approximations of the delayed term. It is shown that if the time-periodic coefficients in the equation are approximated by piecewise constant functions, then there is no need to use higher than first-order approximations of the delayed term. The results are demonstrated on construction of the stability chart of the delayed Mathieu equation.