Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces

DOI10.3792/PJAA.87.109zbMath1236.65060OpenAlexW1995770575MaRDI QIDQ665909

Yuusuke Iso

Publication date: 7 March 2012

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.87.109

zbMATH Keywords

convergencenumerical exampleBanach spacesabstract Cauchy problemfinite difference schemesemidiscretizationill-posed problemsCauchy-Kowalevskaya's theoremmultiple-precision arithmetic

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical solutions to equations with linear operators (65J10) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for first-order hyperbolic systems (35L45) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solutions to abstract evolution equations (65J08)

Related Items (1)

Semi-discrete finite difference schemes for the nonlinear Cauchy problems of the normal form

Cites Work

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• Convergence of finite difference scheme and analytic data
• A note on a theorem of Nirenberg
• Survey of the stability of linear finite difference equations

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