Rigorous Enclosures of Solutions of Neumann Boundary Value Problems

TL;DR

This paper introduces a rigorous method using the Newton-Kantorovich Theorem to enclose and validate solutions of non-linear two-point boundary value problems with Neumann boundary conditions.

Contribution

The paper develops a novel approach for isolating and validating solutions of Neumann boundary value problems using rigorous enclosures based on the Newton-Kantorovich Theorem.

Findings

Successfully encloses solutions of Neumann boundary value problems

Provides a rigorous validation method for zeros of boundary value problems

Enhances solution reliability in nonlinear boundary value analysis

Abstract

This paper is dedicated to the problem of isolating and validating zeros of non-linear two point boundary value problems. We present a method for such purpose based on the Newton-Kantorovich Theorem to rigorously enclose isolated zeros of two point boundary value problem with Neumann boundary conditions.