I. Gyori et al., NUMERICAL APPROXIMATIONS FOR A CLASS OF DIFFERENTIAL-EQUATIONS WITH TIME-DEPENDENT AND STATE-DEPENDENT DELAYS, Applied mathematics letters, 8(6), 1995, pp. 19-24
We establish limiting relations between solutions for a large class of
functional differential equations with time- and state-dependent dela
ys and solutions of appropriately selected sequences of approximating
delay differential equations with piecewise constant arguments. The ap
proximating equations, generated in the above process, lead naturally
to discrete differences equations, well suited for computational purpo
ses, and thus provide and approximation framework for simulation studi
es.