  In this paper we consider a class of boundary value problems for third order
nonlinear functional differential equation. By the reduction of the problem to
operator equation we establish the existence and uniqueness of solution and
construct a numerical method for solving it. We prove that the method is of
second order accuracy and obtain an estimate for total error. Some examples
demonstrate the validity of the obtained theoretical results and the efficiency
of the numerical method. The approach used for the third order nonlinear
functional differential equation can be applied to functional differential
equations of any orders.
