The TrotterKato theorem and approximation of PDEs
Authors:
Kazufumi Ito and Franz Kappel
Journal:
Math. Comp. 67 (1998), 2144
MSC (1991):
Primary 47D05, 47H05, 65J10, 35K22, 35L99
MathSciNet review:
1443120
Fulltext PDF Free Access
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Abstract: We present formulations of the TrotterKato theorem for approximation of linear Csemigroups 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:
http://dx.doi.org/10.1090/S0025571898009156
PII:
S 00255718(98)009156
Keywords:
Semigroups of transformations,
TrotterKatoTheorems,
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 UINT8521208 and DMS8818530 and by the Air Force Office of Scientific Research under contract AFOSR900091.
Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146PHY and under F003.
Article copyright:
© Copyright 1998
American Mathematical Society
