Abstract
It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
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Crouzeix, M., Larsson, S., Piskarev, S. et al. The stability of rational approximations of analytic semigroups. BIT 33, 74–84 (1993). https://doi.org/10.1007/BF01990345
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DOI: https://doi.org/10.1007/BF01990345