The Trotter-Kato theorem and

approximation of PDEs

Authors:
Kazufumi Ito and Franz Kappel

Journal:
Math. Comp. **67** (1998), 21-44

MSC (1991):
Primary 47D05, 47H05, 65J10, 35K22, 35L99

DOI:
https://doi.org/10.1090/S0025-5718-98-00915-6

MathSciNet review:
1443120

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-98-00915-6

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.

Article copyright:
© Copyright 1998
American Mathematical Society