Abstract
This paper sets out a theoretical framework for approximating the attractor A of a semigroup S(t) defined on a Banach space X by a q-step semidiscretization in time with constant steplength k. Using the one-step theory of Hale, Lin and Raugel, sufficient conditions are established for the existence of a family of attractors {A k } ⊂ X q , for the discrete semigroups S k n defined by the numerical method. The convergence properties of this family are also considered. Full details of the theory are exemplified in the context of strictly A(α)-stable linear multistep approximations of an abstract dissipative sectorial evolution equation.
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