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On Approximation by Discrete Semigroups

✍ Scribed by N.H. Abdelaziz

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
496 KB
Volume
73
Category
Article
ISSN
0021-9045

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✦ Synopsis

The present paper deals with the problem of approximation of a continuous parameter semigroup (T(t), t>0) on a Banach space (X) by means of a sequence of discrete parameter semigroups (\left(F_{n}^{k}\right)), where (F_{n}) is a bounded operator on a Banach space (X_{n}, n \in N), and where (\left(X_{n}\right)) and (X) are related in some appropriate sense. This problem arises, e.g., when numerical methods are used to approximate solutions of initial boundary value problems in PDEs. The results obtained here present a new set of tests for convergence of discrete semigroups, which are different from those in (E. GΓΆrlich and D. Pontzen, TΓΆhuku Math. J. (2) 34, No. 4 (1982), 539-552). Theorem 2 and its corollaries extend the earlier results on this point. 1993 Academic Press. Inc.

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