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Rational approximation schemes for solutions of the first and second order Cauchy problem


Author: Patricio Jara
Journal: Proc. Amer. Math. Soc. 137 (2009), 3885-3898
MSC (2000): Primary 65M12, 65M15; Secondary 47D60, 44A45, 47D62
DOI: https://doi.org/10.1090/S0002-9939-09-09891-8
Published electronically: July 10, 2009
MathSciNet review: 2529897
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Abstract: The purpose of this paper is to give sharp error estimates for regularized versions of $ A$-stable rational approximations of $ C$-regularized semigroups such as the Backward Euler and Crank-Nicolson scheme among others. The main tools used are those developed by P. Brenner and V. Thomée for strongly continuous semigroups together with a regularized version of the Hille-Phillips functional calculus.


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Additional Information

Patricio Jara
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: pjara@math.lsu.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09891-8
Keywords: C-regularized semigroups, Hille-Phillips functional calculus, time discretization, Pad\'e approximants, Backward Euler, Crank-Nicolson, RadauIIA
Received by editor(s): August 18, 2008
Received by editor(s) in revised form: November 2, 2008
Published electronically: July 10, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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