A unified approach to study the existence and numerical solution of functional differential equation.

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. • We propose a unified approach to third order nonlinear functional differential equation. • By this method we have established the existence, uniqueness of solution. • We propose a numerical method for finding the solution and prove that its total error is of the second order accuracy. • Many examples demonstrate the applicability of the theoretical results and the efficiency of the numerical method. • The approach can be applied to functional differential equations of any orders. [ABSTRACT FROM AUTHOR]