Crank-Nicolson scheme for abstract linear systems

S. Piskarev, Heiko J. Zwart

    Research output: Contribution to journalArticleAcademicpeer-review

    12 Citations (Scopus)
    4 Downloads (Pure)


    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.
    Original languageUndefined
    Article number10.1080/01630560701380981
    Pages (from-to)717-736
    Number of pages20
    JournalNumerical functional analysis and optimization
    Issue numberLNCS4549/5&6
    Publication statusPublished - 2007


    • Infinite-dimensional system
    • Cayley transform
    • $C_0$-semigroups
    • IR-61889
    • METIS-241852
    • MSC-93C10
    • Crank-Nicolson scheme
    • EWI-10926
    • MSC-46N20
    • MSC-34G10
    • MSC-65J10

    Cite this