  In this paper we consider a fully third order nonlinear boundary value
problem which is of great interest of many researchers. First we establish the
existence, uniqueness of solution. Next, we propose simple iterative methods on
both continuous and discrete levels. We prove that the discrete methods are of
second order and third accuracy due to the use of appropriate formulas for
numerical integration and obtain estimate for total error. Some examples
demonstrate the validity of the obtained theoretical results and the efficiency
of the iterative method.
