Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.