Segmented Tau approximation for a forward–backward functional differential equation

A new approach to numerically solve the forward–backward functional differential equation equation(1)x′(t)=ax(t)+bx(t−1)+cx(t+1),x′(t)=ax(t)+bx(t−1)+cx(t+1), is presented, where aa, bb, and cc are constant parameters. The step by step version of the Tau method is applied to approximate the solution of Eq. (1) by a piecewise polynomial function. A boundary value problem is posed, solved with the proposed method, and analyzed. The numerical results obtained are consistent with those produced by other methods found in the literature.