Numerical solution of a nonlinear functional integro-differential equation

TL;DR

This paper develops a second-order accurate numerical method for solving a boundary value problem involving a nonlinear functional integro-differential equation, with proven existence, uniqueness, and error estimates.

Contribution

It introduces a new numerical approach for a complex nonlinear integro-differential equation and provides theoretical analysis and validation through examples.

Findings

The numerical method is of second order accuracy.

Existence and uniqueness of solutions are established.

The method demonstrates efficiency and reliability in examples.

Abstract

In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential 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 the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.