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 C0-semigroup leads to a bounded discrete-time system. On Hilbert spaces, this result can be extended to all bounded C0-semigroups for which the inverse generator generates a bounded C0-semigroup. The presentation is based on C0-semigroup theory and uses a functional analysis approach.
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