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2010 Fiscal Year Final Research Report

Stability and numerical analysis for delay differential equations

Research Project

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Project/Area Number 20540137
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo University of Science

Principal Investigator

ISHIWATA Emiko  Tokyo University of Science, 理学部, 准教授 (30287958)

Project Period (FY) 2008 – 2010
Keywords遅延微分方程式 / 数値解析 / 大域安定性 / 数理生物モデル
Research Abstract

We obtained some results related to the functional differential equations by this grant. We first derived new global stability conditions for a class of difference equations with time delay. Next, we showed an attainable order of collocation methods for delay differential and Volterra integral equations with proportional delay. Super attainable order was also considered. Finally, we considered some global stability for epidemic models with time delay. Using a discretization of combined explicit with implicit schemes, we obtained the global dynamics of a discretized SIRS epidemic model with time delay, corresponding to that of continuous model.

  • Research Products

    (13 results)

All 2010 2009 2008 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (5 results) Remarks (1 results)

  • [Journal Article] Global dynamics of a discretized SIRS epidemic model with time delay2010

    • Author(s)
      Masaki Sekiguchi, Emiko Ishiwata
    • Journal Title

      J.Math.Anal.Appl. 371

      Pages: 195-202

    • Peer Reviewed
  • [Journal Article] On the qd-type discrete hungry Lotka-Volterra system and its application to the matrix eigenvalue algorithm2009

    • Author(s)
      Akiko Fukuda, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura
    • Journal Title

      JSIAM Letters 1

      Pages: 36-39

    • Peer Reviewed
  • [Journal Article] Stability for a class of difference equations2009

    • Author(s)
      Yoshiaki Muroya, Emiko Ishiwata
    • Journal Title

      J.Comput.Appl.Math. 228

      Pages: 561-570

    • Peer Reviewed
  • [Journal Article] New global stability conditions for a class of difference equations2009

    • Author(s)
      Yoshiaki Muroya, Emiko Ishiwata, Nicola Guglielmi
    • Journal Title

      Front.Math.Comp. 4,no,1

      Pages: 131-154

    • Peer Reviewed
  • [Journal Article] On collocation methods for delay differential and Volterra integral equations with proportional delay2009

    • Author(s)
      Emiko Ishiwata, Yoshiaki Muroya
    • Journal Title

      Front.Math.Comp. 4,no,1

      Pages: 89-111

    • Peer Reviewed
  • [Journal Article] The discrete hungry Lotka-Volterra system and a new algorithm for computing matrix eigenvalues2009

    • Author(s)
      Akiko Fukuda, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura
    • Journal Title

      Inverse Problems 25

      Pages: 015007

    • Peer Reviewed
  • [Journal Article] A super-attainable order of collocation methods for differential equations with proportional delay2008

    • Author(s)
      Emiko Ishiwata, Yoshiaki Muroya, Hermann Brunner
    • Journal Title

      Appl.Math.Comp. 198

      Pages: 227-236

    • Peer Reviewed
  • [Presentation] Global dynamics of a discretized SIRS epidemic model with time delay and its applications2010

    • Author(s)
      Dai Okada, Masaki Sekiguchi, Emiko Ishiwata
    • Organizer
      3rd China-Japan Colloquium of Mathematical Biology (CJCMB3)
    • Place of Presentation
      Sea North Green Garden-Beijing, China(poster)
    • Year and Date
      20101018-20101021
  • [Presentation] 定期的なワクチン接種を考慮した時間遅れを含む離散型SIRモデルの大域的挙動2009

    • Author(s)
      関口真基,石渡恵美子
    • Organizer
      日本数学会応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      20091200
  • [Presentation] 離散ハングリー可積分系に基づく帯行列の固有値計算アルゴリズム2009

    • Author(s)
      福田亜希子,石渡恵美子,岩崎雅史,中村佳正
    • Organizer
      日本数学会2009年度秋季総合分科会応用数学分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      20090900
  • [Presentation] 離散ハングリー可積分系による固有値計算アルゴリズムとその漸近挙動2008

    • Author(s)
      福田亜希子,石渡恵美子,岩崎雅史,中村佳正
    • Organizer
      日本数学会応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      20081200
  • [Presentation] ある種の差分方程式の安定性について2008

    • Author(s)
      石渡恵美子
    • Organizer
      日本応用数理学会平成20年度年会オーガナイズドセッション「生物システムの安定性」
    • Place of Presentation
      東京大学
    • Year and Date
      20080900
  • [Remarks] ホームページ等

    • URL

      http://www.tus.ac.jp/fac/teacher/achievement.php?A05511

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Published: 2012-01-26   Modified: 2016-04-21  

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