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In this paper we consider a fully third order nonlinear boundary valueproblem which is of great interest of many researchers. First we establish theexistence, uniqueness of solution. Next, we propose simple iterative methods onboth continuous and discrete levels. We prove that the discrete methods are ofsecond order and third accuracy due to the use of appropriate formulas fornumerical integration and obtain estimate for total error. Some examplesdemonstrate the validity of the obtained theoretical results and the efficiencyof the iterative method.

A simple numerical method of second and third orders convergence for solving a fully third order nonlinear boundary value problem