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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Upper semicontinuity of attractors for linear multistep methods approximating sectorial evolution equations
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by Adrian T. Hill and Endre Süli PDF
Math. Comp. 64 (1995), 1097-1122 Request permission


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.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1097-1122
  • MSC: Primary 65J05; Secondary 34G20, 47H20, 47N20, 58F13, 65L06, 65M12
  • DOI:
  • MathSciNet review: 1297470