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math.NA2000★ 1 cited
A holistic finite difference approach models linear dynamics consistently
A. J. Roberts
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamica…
math.DS2000★ 3 cited
A flexible error estimate for the application of centre manifold theory
Zhenquan Li, A. J. Roberts
In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend…