Crank-Nicolson scheme for abstract linear systems

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Piskarev, S. and Zwart, H.J. (2007) Crank-Nicolson scheme for abstract linear systems. Numerical Functional Analysis and Optimization, 28 (5&6). pp. 717-736. ISSN 0163-0563

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Abstract:This paper studies the Crank-Nicolson discretization scheme for abstract differential equations on a general Banach space. We show that a time varying discretization of a bounded analytic $C_0$-semigroups leads to a bounded discrete-time system. On Hilbert spaces this result can be extended to all bounded $C_0$-semigroups for which the inverse generator generates a bounded $C_0$-semigroup. The presentation is based on $C_0$-semigroup theory and uses a functional analysis approach.
Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/61889
Official URL:http://dx.doi.org/10.1080/01630560701380981
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