Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo

• Ano de defesa: 2015
• Autor(a) principal: Maio, Pablo Aguiar de
• Orientador(a): Cruz Cancino, Hugo Alexander de la
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Equações diferenciais estocásticas; Esquemas exponenciais de Linearização local; Passo adaptativo; A-estabilidade; Análise numérica; Simulação computacional
• Palavras-chave em Inglês: Stochastic differential equations; Local Linearization Exponential schemes; A-stability; Numerical analysis; Computer simulation; Adaptive stepsize
• Link de acesso: http://hdl.handle.net/10438/14095

In this work we present a new numerical method with adaptive stepsize based on the local linearization approach, to integrate stochastic differential equations with additive noise. We also propose a computational scheme that allows efficient implementation of this method, properly adapting the algorithm of Padé with scaling-squaring strategy to compute the exponential of matrices involved. To introduce the construction of this method, we briefly explain what stochastic differential equations are, the mathematics that is behind them, their relevance to the modeling of various phenomena, and the importance of using numerical methods to evaluate this kind of equations. A succinct study of numerical stability is also presented on the following pages. With this dissertation, we intend to introduce the necessary basis for the construction of the new method/scheme. At the end, several numerical experiments are performed to demonstrate, in a practical way, the effectiveness of the proposed method, comparing it with other methods commonly used.