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July 2011 Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces
Yuusuke Iso
Proc. Japan Acad. Ser. A Math. Sci. 87(7): 109-113 (July 2011). DOI: 10.3792/pjaa.87.109

Abstract

We show convergence of a finite difference scheme to solve the abstract Cauchy problem on a scale of Banach spaces which includes that for Kowalevskaya’s system. We show convergence of consistent difference schemes even for unstable cases.

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Yuusuke Iso. "Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces." Proc. Japan Acad. Ser. A Math. Sci. 87 (7) 109 - 113, July 2011. https://doi.org/10.3792/pjaa.87.109

Information

Published: July 2011
First available in Project Euclid: 7 July 2011

zbMATH: 1236.65060
MathSciNet: MR2821574
Digital Object Identifier: 10.3792/pjaa.87.109

Subjects:
Primary: 65M12
Secondary: 35A10 , 65J10

Keywords: Cauchy-Kowalevskaya’s theorem , finite difference scheme , Ill-posed problems , multiple-precision arithmetic , Numerical analysis for partial differential equations

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 7 • July 2011
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