Abstract:

An optimization method was used to calculate the periodic solutions of delay differential equations. The method transforms the computation of periodic solutions of delayed differential equation into an optimization problem with constraints. Using the optimization method, we can get the periodic solutions. Numerically, we proposed a method to get approximately the initial function via function fitting methods, and further used Newton’s method and penalty function method to locate the periodic solutions. Numerical experiments verify the effectiveness and efficiency of the proposed algorithm.

Key words: time delay, optimization, periodic solution, initial functions