EMBEDDING OF DELAY EQUATIONS INTO AN INFINITE-DIMENSIONAL ODE SYSTEM

A technique is introduced to embed the solution of the delay different ial equation y'(t) = F(t, y(t), y(theta(t))), y(0) = y(0), into an inf inite ODE system. This embedding is a starting point to deduce theorem s on asymptotic stability of y, as well as to the construction of two numerical methods. The first method operates on a ''natural gird,'' wh ich is generated by iterating the lag function theta, and it is accomp anied by estimates on its speed of convergence. The second method cons ists of an application of standard ODE solvers to a truncated embeddin g. Its main merit is that the special structure of the embedded ODE sy stem can be exploited in a massively parallel implementation. (C) 1995 Academic Press, Inc.