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We present an algorithm for the rigorous integration of Delay DifferentialEquations (DDEs) of the form $x'(t)=f(x(t-\tau),x(t))$. As an application, wegive a computer assisted proof of the existence of two attracting periodicorbits (before and after the first period-doubling bifurcation) in theMackey-Glass equation.

Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation