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Master's Dissertation
DOI
10.11606/D.55.2018.tde-27112018-103407
Document
Author
Full name
José Eduardo Castilho
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1991
Supervisor
Committee
Cuminato, José Alberto (President)
Boldrini, José Luiz
Meneguette Junior, Messias
Title in Portuguese
ESTABILIDADE NÃO LINEAR DE EQUAÇÕES A DERIVADAS PARCIAIS DO TIPO PARABÓLICO
Keywords in Portuguese
Não disponível
Abstract in Portuguese
O objetivo principal deste trabalho é descrever a manifestação da instabilidade numérica em problemas de Reação-Difusão. Uma análise conjunta do problema continuo e sua discretização mostra claramente onde e quando a discretização falha. Esta análise fornece um conhecimento básico para a interpretação da instabilidade numérica em equações diferenciais parciais parabólicas não lineares. Os problemas, continuo e discreto, são analisados através da teoria da bifurcação local, estabilidade linear e estabilidade não linear fraca. Mostra-se que a instabilidade numérica está associada com a bifurcação periódica no problema discreto, fato que não ocorre no problema contínuo. Isto é ilustrado através de exemplos numéricos.
Title in English
Non-linear stability of  parabolic partial differential equations
Keywords in English
Not available
Abstract in English
The main purpose of this work is to describe the manisfetation of numerical instability in Reaction-Diffusion problems. A unified analysis of the continuous problem and its discretisation shows clearly when and why the discretisation breaks down. This analysis provides background for interpretation of numerical instability in nonlinear parabolic partial differential equations. The problems, continuous and discrete, are analysed from the points of view of local bifurcation, linear stability and weakly nonlinear stability theories. It is shown that numerical instability is associated with the bifurcation of periodic orbits in the discrete problems, a fact that does not happen in the continuous case. Numerical examples that illustrate the various possibilities are presented and analysed in light of this theory.
 
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Publishing Date
2018-11-27
 
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