On exponential dichotomy and frameworks for rigorous computation for differential equations

• Ano de defesa: 2023
• Autor(a) principal: Nakassima, Guilherme Kenji
• 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: Combinatorial marching hypercubes; Dicotomia exponencial; Exponential dichotomy; Haar wavelets; Métodos computacionais rigorosos; Rigorous computational methods; Robustez da estabilidade; Robustness of stability; Wavelet de Haar
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-16012024-160656/

In this work we show research results on three different topics: robustness of asymptotic stability and exponential dichotomy for a class of differential equations in Banach spaces; a wavelet-based approach for a-posteriori self-validating numerical methods for differential equations, using the radii polynomial method; and the Generalized Combinatorial Marching Hypercubes algorithm for generation of manifolds in high dimensions, using combinatorial techniques to improve computational efficiency.