Zeros dos Polinômios Característicos dos Métodos BDF
DOI:
https://doi.org/10.5540/tema.2007.08.01.0093Abstract
O estudo da estabilidade de métodos numéricos possui um grande potencial em pesquisa. Como a análise da estabilidade está relacionada aos zeros do polinômio característico do método, é importante determinar o comportamento de tais zeros. Através de testes numéricos é possível verificar facilmente que os zeros dos polinômios característicos dos métodos BDF são distintos (para K fixo). Mas a prova da validade deste resultado para toda a família dos métodos, nunca feita anteriormente, será apresentada neste trabalho com o uso das order stars, que são conjuntos que definem uma partição no plano complexo.References
A. Iserles, S.P. Nørsett, A proof of the first Dahlquist barrier by order stars, BIT, 24 (1984), 529-537.
A. Iserles, S.P. Nørsett,“Order Stars”, Chapman and Hall, London, 1991.
R. Jeltsch, A0−stability and stiff stability of Brown´s multistep multiderivative methods, Numer. Math. 32 (1979), 167-181.
M. Meneguette Jr., “Multistep Multiderivative Methods and Related Topics”, Tese de Doutorado, Oxford, UK, 1987.
G. Wanner, E. Hairer, S.P. Nørsett, Order stars and stability theorems, BIT, 18 (1978), 475-489.
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