We present a new approach for the numerical solution of DDEs different from the classical step-by-step method. We restate a DDE as an abstract Cauchy problem (or as an hyperbolic PDE with a particular non standard boundary condition) and then we discretize it, by a class of schemes, in a system of ODEs. Since this approach allows using stepsizes larger than delay, it can be advantageous for DDEs with large integration window, small delay and smooth solution. Moreover, from the asymptotic stability point of view, the new method seems to work where the classical method does not (i.e. linear systems of DDEs for "fixed delay" ).

MINISIMPOSIUM SESSION: 3. Numerical methods for delay equations (2 sessions)