Existence results and numerical solution of fully fourth order nonlinear functional differential equations

TL;DR

This paper proves the existence and uniqueness of solutions for a class of complex fourth order nonlinear functional differential equations and develops efficient numerical methods with error estimates.

Contribution

It introduces new existence and uniqueness results and constructs iterative numerical methods for solving fully fourth order nonlinear functional differential equations.

Findings

Proved existence and uniqueness of solutions.

Developed iterative methods with error estimates.

Validated methods with numerical examples.

Abstract

In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation for the right hand side nonlinear function we establish the existence and uniqueness of solution and construct iterative methods on both continuous and discrete levels for solving it. We obtain the total error estimate for the discrete iterative solution. Many examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.