Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Upper semicontinuity of attractors for linear multistep methods approximating sectorial evolution equations

Authors: Adrian T. Hill and Endre Süli
Journal: Math. Comp. 64 (1995), 1097-1122
MSC: Primary 65J05; Secondary 34G20, 47H20, 47N20, 58F13, 65L06, 65M12
MathSciNet review: 1297470
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper sets out a theoretical framework for approximating the attractor $ \mathcal{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 $ \{ {\mathcal{A}_k}\} \subset {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(\alpha )$-stable linear multistep approximations of an abstract dissipative sectorial evolution equation.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65J05, 34G20, 47H20, 47N20, 58F13, 65L06, 65M12

Retrieve articles in all journals with MSC: 65J05, 34G20, 47H20, 47N20, 58F13, 65L06, 65M12

Additional Information

Keywords: Numerical analysis in abstract spaces, approximation of attractors, multistep methods, error bounds and convergence of numerical methods
Article copyright: © Copyright 1995 American Mathematical Society