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| Author(s): |
Victor Hugo Nolasco
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2022-08-24 |
| Examining board members: |
Márcio Fuzeto Gameiro;
Antonio Castelo Filho;
Savio Brochini Rodrigues;
Paulo Leandro Dattori da Silva
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| Advisor: | Márcio Fuzeto Gameiro |
| Abstract | |
Although constant evolution of existing computational methods, the problem of solve ordinary differential equations still quite pertinent, since such equations model phenomenas that are fundamental to the development of science, and as a consequence, of society. In order to collaborate to solve this problem, this work provides method of enclosure solutions for systems of ordinary differential equations. This aim includes theoretical aspects, abstract reformulation of the differential equation in infinite dimension spaces, and its consequences, and practical, implementation of code that rigorously checks the hypotheses of the theoretical results obtained. As a result, we rigorously enclosure solutions for systems of ordinary differential equations for initial values problems and boundary values problems in linear and non-linear cases, based on Newton-Kantorovichs Theorem. Unlike the other rigorous numerics methods, our method provides an initial guess for numerical solution, something that is difficult to obtain in the case of non-linear differential equations, and does not require great changes for different types of non-linearities. (AU) | |
| FAPESP's process: | 13/14770-2 - Rigorous Continuation Using Fourier-Chebyshev Basis |
| Grantee: | Victor Hugo Nolasco |
| Support Opportunities: | Scholarships in Brazil - Doctorate |