NUMERICAL APPROXIMATIONS FOR A CLASS OF DIFFERENTIAL-EQUATIONS WITH TIME-DEPENDENT AND STATE-DEPENDENT DELAYS

We establish limiting relations between solutions for a large class of functional differential equations with time- and state-dependent delays and solutions of appropriately selected sequences of approximating delay differential equations with piecewise constant arguments. The approximating equations, generated in the above process, lead naturally to discrete differences equations, well suited for computational purposes, and thus provide and approximation framework for simulation studies.