Upper Semicontinuity of Attractors for Linear Multistep Methods
نویسنده
چکیده
This paper sets out a theoretical framework for approximating the attractor A of a semigroup S(t) deened on a Banach space X by a q{step semi{discretization in time with constant step{length k. Using the one{step theory of Hale, Lin and Raugel, suucient conditions are established for the existence of a family of attractors fA k g X q , for the discrete semigroups S n k deened by the numerical method. The convergence properties of this family are also considered. Full details of the theory are exempliied in the context of strictly A(){stable linear multistep approximations of an abstract dissipative sectorial evolution equation.
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Upper Semicontinuity of Attractors for Linear Multistep Methods Approximating Sectorial Evolution Equations
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