BIT Numerical Mathematics

, Volume 33, Issue 1, pp 74–84

The stability of rational approximations of analytic semigroups

  • M. Crouzeix
  • S. Larsson
  • S. Piskarev
  • V. Thomée
Part II Numerical Mathematics

DOI: 10.1007/BF01990345

Cite this article as:
Crouzeix, M., Larsson, S., Piskarev, S. et al. BIT (1993) 33: 74. doi:10.1007/BF01990345

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)

65J1065M12

Key words and phrases

Analytic semigroupBanach spacerational approximationA-acceptableA(θ)-acceptablestability Crank-Nicolson method

Copyright information

© BIT Foundations 1993

Authors and Affiliations

  • M. Crouzeix
    • 1
  • S. Larsson
    • 2
  • S. Piskarev
    • 2
  • V. Thomée
    • 2
  1. 1.Institut Mathématique et IRISAUniversité de Rennes IRennes CedexFrance
  2. 2.Department of MathematicsChalmers University of TechnologyGöteborgSweden