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In this paper we consider a class of boundary value problems for third ordernonlinear functional differential equation. By the reduction of the problem tooperator equation we establish the existence and uniqueness of solution andconstruct a numerical method for solving it. We prove that the method is ofsecond order accuracy and obtain an estimate for total error. Some examplesdemonstrate the validity of the obtained theoretical results and the efficiencyof the numerical method. The approach used for the third order nonlinearfunctional differential equation can be applied to functional differentialequations of any orders.

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