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

TL;DR

This paper proves the existence and uniqueness of solutions for a class of fourth order nonlinear integro-differential equations with Navier boundary conditions and introduces a second-order accurate numerical method.

Contribution

It establishes theoretical existence and uniqueness results and develops a new second-order numerical method for solving these complex equations.

Findings

Existence and uniqueness of solutions proven

Numerical method is of second order accuracy

Method demonstrated to be efficient through examples

Abstract

In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.