Parameterization and Trigonometric Approximation of Periodic Solutions of Non-linear Equations with Deviating Arguments

A constructive approach is proposed for the approximate finding of periodic solutions of differential systems with deviating argument and non-linearities satisfying the Lipschitz condition in a bounded region. Under suitable assumptions, the method allows one to prove solvability based on computational results. We describe a computationally less demanding version of the scheme involving trigonometric polynomial interpolation, in which higher-order approximations are constructed without symbolic integration. The practical use of the method is demonstrated with numerical examples.