On The Enclosure of Solutions of Nonlinear Equations in Banach Space with Application to Boundary Value Problems

• Ano de defesa: 2019
• Autor(a) principal: Ramos, Eduardo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Condição de contorno de Neumann; Equações diferenciais; Inexact Newton method; Matemática verificativa; Método de Newton inexato; Neumann boundary condition; Nonlinear equation solutions; Rigorous numerics; Soluções de equações não lineares; Two point boundary value problem
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-04022020-113120/

This paper is dedicated to the problem of isolating zeros of non-linear equations in closed balls of Bannach spaces. Thus, in this thesis we shall present an algorithm with such purpose, with terminating guarantees, under certain compatibility and regularity conditions of the function that represents the equation. We shall also present a new theorem for the feasibility and convergence of the Inexact Newton Method, such that the error committed does not necessarily must go to zero for the method to be feasible, where this conditions is usually imposed other works. This results is, to the best of the author knowledge, the first of this kind in the literature. Finally, we shall show how to apply the proposed zero isolation algorithm and the Inexact Newton Method to enclosure and approximate zeros of two point boundary value problem of Neumann type.