Numerical solution for a family of delay functional differential equations using step by step Tau approximations

We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations begin{eqnarray} nonumber a_1(t)y'(t) & = & y(t)[a_2(t)y(t-tau)+a_3(t)y'(t-tau) + a_4(t)] nonumber & & + ; a_5(t)y(t-tau) + a_6(t)y'(t-tau)+ a_7(t), ;;; tgeq 0 nonumber y(t) & = & Psi(t),;;;; tleq 0 nonumber end{eqnarray} which represents, for particular values of $a_i(t)$, $i=1,7$, and $tau$, functional differential equations that arise in a natural way in different areas of applied mathematics. This paper means to highlight the fact that the step by step Tau method is a natural and promising strategy in the numerical solution of functional differential equations.