Computational method for a fourth order nonlinear elliptic boundary value problem

Abstract

In this paper we consider a boundary value problem for a fourth order nonlinear elliptic equation, which models a bending plate on nonlinear elastic foundation. Differently from other authors, here we propose a novel approach to investigation of solvability and numerical solution of the problem. Namely, we reduce it to an operator equation for the right hand side function and under some easily verified conditions we have established the existence and uniqueness of a solution. We have also constructed an iterative method for the solution of the problem. The theoretical results are illustrated on several examples, where the advantages in convergence rate of the method over other methods are shown.