Numerical Solution of a Fully Fourth Order Nonlinear Problem

摘要

In this paper we consider a fully fourth order nonlinear boundary value problem which models a statistically bending elastic beam. Differently from the approaches of the other authors, we reduce the problem to an operator equation for the right-hand side function. The existence and uniquenness of solution is established. Besides, we propose an iterative method for solving the problem. Some numerical examples demonstrate the efficiency of the method.