Validate Computation Library on Time Evolution Equations

2011 Fiscal Year Final Research Report

• Project/Area Number: 21540115
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Electro-Communications
• Principal Investigator: YAMAMOTO Nobito 電気通信大学, 大学院・情報理工学研究科, 教授 (30210545)
• Co-Investigator(Kenkyū-buntansha): NAKAMURA Ken-ichi 金沢大学, 理工研究域数物科学系, 准教授 (40293120) ; OGATA Hidenori 電気通信大学, 大学院・情報理工学研究科, 准教授 (50242037)
• Project Period (FY): 2009 – 2011
• Keywords: 精度保証 / 発展方程式 / 多倍長演算 / プログラム自動生成 / 常微分方程式

Research Abstract

We have investigated in computer program library including validated computation techniques which give the basis of validated computation of time evolution equations, and derived a number of new approaches to numerical verification of ODEs which appear as semi-discretized equations of PDEs. The results were published in academic journals.

Research Products

• [Journal Article] Validated Computation of Global Solutions to ODEs (2013)
  • Author(s): M. Harikae, N. Yamamoto
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: Vol.4, No.1 Pages: 88-96
  • URL: http://dx.doi.org/10.1587/nolta.4.88
• [Journal Article] 力学系における閉軌道の存在領域の精度保証法による同定 (2012)
  • Author(s): 樋脇知広・山本野人
  • Journal Title: 日本応用数理学会論文誌 Volume: Vol.22, No.4 Pages: 269-276
• [Journal Article] On the basic operations of interval multiple-precision arithmetic with center-radius form (2011)
  • Author(s): N. Matsuda, N. Yamamoto
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: Vol.2, No.1 Pages: 54-67
  • URL: http://dx.doi.org/10.1587/nolta.2.54
• [Journal Article] An Application of Taylor Models to the Nakao Method on ODEs (2009)
  • Author(s): N.Yamamoto, T.Komori
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 26, No.1 Pages: 365-392
• [Presentation] Validated Computation of Global Solutions to ODEs (2011)
  • Author(s): N. Yamamoto, M. Harikae
  • Organizer: the Japan-German Workshop on Computer-Assisted proofs and Verification Methods
  • Place of Presentation: Karisruhe,Germany
  • Year and Date: 20110918-22
• [Presentation] Interval Multiple-Precision Arithmetic with center-radius form (2010)
  • Author(s): N. Yamamoto, N. Matsuda
  • Organizer: SCAN2010, 14th GAMM-IMACS, International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
  • Place of Presentation: ENS de Lyon, Francs
  • Year and Date: 20100927-30
• [Book] 「精度保証の手法」、現代数理科学事典第2 版IX 章第6節 (2009)
  • Author(s): 山本野人
  • Publisher: 丸善