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The Trotter-Kato theorem and approximation of PDEs
Author(s):
Kazufumi
Ito;
Franz
Kappel.
Journal:
Math. Comp.
67
(1998),
21-44.
MSC (1991):
Primary 47D05, 47H05, 65J10, 35K22, 35L99
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Abstract:
We present formulations of the Trotter-Kato theorem for approximation of linear C -semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes' equation as illustrative examples.
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Additional Information:
Kazufumi
Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
Email:
kito@eos.ncsu.edu
Franz
Kappel
Affiliation:
Institut für Mathematik, Universität Graz, Heinrichstraße 36, A8010 Graz, Austria
Email:
franz.kappel@kfunigraz.ac.at
DOI:
10.1090/S0025-5718-98-00915-6
PII:
S 0025-5718(98)00915-6
Keywords:
Semigroups of transformations,
Trotter-Kato-Theorems,
numerical approximation of linear evolutionary equations
Received by editor(s):
August 18, 1995
Received by editor(s) in revised form:
August 1, 1996
Additional Notes:
Research of the first author was supported in part by the NSF under Grant UINT-8521208 and DMS-8818530 and by the Air Force Office of Scientific Research under contract AFOSR-90-0091.
Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146-PHY and under F003.
Copyright of article:
Copyright
1998,
American Mathematical Society
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