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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Some discrete inequalities for central-difference type operators
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by Hiroki Kojima, Takayasu Matsuo and Daisuke Furihata PDF
Math. Comp. 86 (2017), 1719-1739 Request permission

Abstract:

Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play a key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a systematic approach for deriving such inequalities for a certain class of central-difference type operators. We illustrate the results by giving a generic a priori estimate for certain conservative schemes for the nonlinear Schrödinger and Cahn–Hilliard equations.
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Additional Information
  • Hiroki Kojima
  • Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Japan
  • Email: hiroki_kojima@mist.i.u-tokyo.ac.jp, h.k.psi.mot@gmail.com
  • Takayasu Matsuo
  • Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Japan
  • MR Author ID: 664782
  • Email: matsuo@mist.i.u-tokyo.ac.jp
  • Daisuke Furihata
  • Affiliation: Cybermedia Center, Osaka University, 1-32 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan
  • MR Author ID: 601502
  • Email: furihata@cmc.osaka-u.ac.jp
  • Received by editor(s): February 16, 2015
  • Received by editor(s) in revised form: November 28, 2015
  • Published electronically: September 15, 2016
  • Additional Notes: This work was supported by JSPS KAKENHI Grant Number 23560063 and 25287030. This work was also supported by CREST, JST
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1719-1739
  • MSC (2010): Primary 65M06, 65M12
  • DOI: https://doi.org/10.1090/mcom/3154
  • MathSciNet review: 3626534