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In this paper we consider a class of fourth order nonlinearintegro-differential equations with Navier boundary conditions. By thereduction of the problem to operator equation we establish the existence anduniqueness of solution and construct a numerical method for solving it. Weprove that the method is of second order accuracy and obtain an estimate fortotal error. Some examples demonstrate the validity of the obtained theoreticalresults and the efficiency of the numerical method.

Existence results and iterative method for solving a fourth order nonlinear integro-differential equation