Comparison of zeroth- and first-order semi-discretizations for the delayed Mathieu equation

Semi-discretization method is applied to construct stability charts for periodic delay-differential equations. Zeroth-, improved zeroth- and first-order methods are used to construct approximate finite dimensional Floquet transition matrices for the delayed Mathieu equation and stability charts are determined. Since the stability boundaries of the delayed Mathieu equation are known in closed form, the convergence of different order approximations can be studied by computer simulations. Stability boundaries and computation times obtained by different time steps and different orders are compared.