  The segmented formulation of the Tau method is used to numerically solve the
non-autonomous forward-backward functional differential equation x'(t) =
a(t)x(t) + b(t)x(t-1) + c(t)x(t+1), where x is the unknown function, a, b, and
c are known functions. The step by step Tau method is applied to approximate
the solution of this equation by a piecewise polynomial function. A boundary
value problem is posed, numerically solved, and analyzed. Also, a novel way to
generate a set of non-autonomous problems with known analytical solution is
provided. From it, several non-autonomous problems were constructed and
resolved with the proposed method. We conclude that the good numerical results
obtained in our numerical experimentation and the relative simplicity of the
Tau method demonstrate that it is a promising strategy for numerically solving
mixed-type problems, as presented here.
