Title
On the Crank-Nicolson scheme once again On the Crank-Nicolson scheme once again
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Source (journal)
Journal of evolution equations. - Basel
Volume/pages
11(2011) :2 , p. 457-476
ISSN
1424-3199
ISI
000290729500009
Carrier
E
Target language
Dutch (dut)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Let jjN be a sequence of strictly positive real numbers, and let A be the generator of a bounded analytic semigroup in a Banach space X. Put An=nj=1I+21jAI−21jA−1 , and let xX. Define the sequence xnnNX by the CrankNicolson scheme: x n = A n x. In this paper, it is proved that the CrankNicolson scheme is stable in the sense that supnNAnx . Some convergence results are also given.
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