Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 33, Issue 1, pp 74-84

The stability of rational approximations of analytic semigroups

  • M. CrouzeixAffiliated withInstitut Mathématique et IRISA, Université de Rennes I
  • , S. LarssonAffiliated withDepartment of Mathematics, Chalmers University of Technology
  • , S. PiskarevAffiliated withDepartment of Mathematics, Chalmers University of Technology
  • , V. ThoméeAffiliated withDepartment of Mathematics, Chalmers University of Technology

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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.

1980 Mathematics Subject Classification (1985 Revision)

65J10 65M12

Key words and phrases

Analytic semigroup Banach space rational approximation A-acceptable A(θ)-acceptable stability Crank-Nicolson method