Segmented Tau approximation for a forward-backward functional differential equation
A new approach to numerically solve the forward-backward functional differential equation x'(t) = ax(t) + bx(t - 1) + cx(t + 1), (1) is presented, where a, b, and c 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. (C) 2011 Elsevier Ltd. All rights reserved.
forward-backward functional differential equation step by step tau method approximation tau method approximation numerical functional differential equation