Numerical solution for a family of delay functional differential equations using step by step tau approximations (Q1653933)

Summary: We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations \[ \begin{aligned} a_1(t)y'(t) &= y(t)[a_2(t)y(t-\tau)+a_3(t)y'(t-\tau) + a_4(t)] \\ & + \; a_5(t)y(t-\tau) + a_6(t)y'(t-\tau)+ a_7(t), \quad t\geq 0 \\ y(t) &= \Psi(t), \quad t\leq 0\end{aligned} \] 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.