Systems of differential equations of higher dimension and delay equations (Q1935736)

This paper deals with the approximation problem of the solution to a delay differential equation \[ \begin{aligned} y'(t)&=-\theta y(t) +g(t-\tau, y(t-\tau)),\quad t>\tau,\\ y(t)& \equiv 0,\quad 0\leq t\leq \tau\end{aligned} \] by the solutions to a sequence of systems of ordinary differential equations \[ \begin{aligned} x'(t) &= A_nx(t) + F_n(t, x),\quad n\gg 1,\\ x(0) &= 0,\end{aligned} \] where \(A_n\) is an \(n\times n\) matrix. Under certain conditions, it is shown that the sequence of the \(n\)th components \(\{x_n(t)\}\) converges to \(y(t)\) uniformly on \([0, T]\) as \(n\to\infty\). This is a continuation of the author's previous work in this area.