Construction of "look-ahead" linear multistep methods for ODEs

• Project/Area Number: 21540153
• 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: Doshisha University
• Principal Investigator: MITSUI Taketomo 同志社大学, 理工学部, 教授 (50027380)
• Co-Investigator(Renkei-kenkyūsha): ESAKI Nobuyuki 豊田工業高等専門学校, 准教授 (80311033)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数値数学 / 微分方程式 / 数値解析 / 離散変数法 / 収束性 / 安定性 / 事後誤差評価 / 数値計算ソフトウェア / 数理モデリング

Research Abstract

We proposed "look-ahead" linear multistep methods as a new type of discrete variable method of initial-value problems of ordinary differential equations by analyzing their numerical properties, and derived several "look-ahead" linear two-step methods, whose convergence and stability are confirmed through numerical experiments. Thus the new method is promising to be competitive with the conventional methods.

Research Products

• [Journal Article] Two-step family of "look-ahead" linear multistep methods for ODEs (2011)
  • Author(s): T. Mitsui, D. Yakubu
  • Journal Title: 同志社大学理工学研究報告 Volume: 52巻 Pages: 181-188
  • NAID: 110008694428
  • Peer Reviewed
• [Journal Article] Two-step family of "look-ahead" linear multistep methods for ODEs (2011)
  • Author(s): T.Mitsui, D.Yakubu
  • Journal Title: 同志社大学理工学研究報告 Volume: 52 Pages: 181-188
  • NAID: 110008694428
  • Peer Reviewed
• [Journal Article] Look-ahead linear multistep methods for ordinary differential equations-Introduction of the method (2010)
  • Author(s): T. Mitsui
  • Journal Title: 同志社大学理工学研究報告 Volume: 51巻 Pages: 181-190
  • NAID: 110007767450
  • Peer Reviewed
• [Journal Article] "Look-ahead" linear multistep methods for ordinary differential equations---Introduction of the method--- (2010)
  • Author(s): T.Mitsui
  • Journal Title: 同志社大学理工学研究報告 Volume: 51 Pages: 181-190
  • NAID: 110007767450
  • Peer Reviewed
• [Journal Article] A pre-fetched BiCGSTAB method in the solution of the trapezoidal rule of large ODEs (2009)
  • Author(s): S. Nakamura, T. Mitsui
  • Journal Title: Far East Journal of Applied Mathematics Volume: 36巻 Pages: 1-24
  • Peer Reviewed
• [Journal Article] A pre-fetched BiCGSTAB method in the solution of the trapezoidal rule of large ODEs (2009)
  • Author(s): S.Nakamura, T.Mitsui
  • Journal Title: Far East Journal of Applied Mathematics 36 Pages: 1-24
  • Peer Reviewed
• [Presentation] Two-step Family of "Look-ahead" Linear Multistep Method for ODEs (2012)
  • Author(s): T. Mitsui, D. Yakubu
  • Organizer: 5th International Conference on High Performance Scientific Computing
  • Place of Presentation: Hanoi理工科大学, Hanoi, Vietnam
  • Year and Date: 2012-03-06
• [Presentation] Two-step Family of "Look-ahead" Linear Multistep Method for ODEs (2012)
  • Author(s): T.Mitsui, D.Yakubu
  • Organizer: 5th International Conference on High Performance Scientific Computing
  • Place of Presentation: Vietnam Institute for Advanced Study in Mathematics, (Hanoi, Vietnam)
  • Year and Date: 2012-03-06
• [Presentation] 常微分方程式に対する"先読み'"線型2段階法の族 (2011)
  • Author(s): T. Mitsui, D. Yakubu
  • Organizer: 応用数学合同研究集会(日本数学会応用数学分科会主催)
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2011-12-16
• [Presentation] スポーツ利用による損傷を考慮した芝生の成長モデル (2011)
  • Author(s): 江崎信行・三井斌友
  • Organizer: 日本応用数理学会2011年度年会
  • Place of Presentation: 同志社大学今出川キャンパス
  • Year and Date: 2011-09-15
• [Presentation] Two-step family of "look-ahead" linear multistep methods for ODEs (2010)
  • Author(s): T. Mitsui, D. Yakubu
  • Organizer: Eighth International Conference on Numerical Analysis and Applied Mathematics(ICNAAM2010)
  • Place of Presentation: Rhodes Palace Hotel, Rhodes, Greece
  • Year and Date: 2010-09-20
• [Presentation] Two-step family of "look-ahead" linear multistep methods for ODEs (2010)
  • Author(s): T.Mitsui, D.Yakubu
  • Organizer: Eighth International Conference on Numerical An alysis and Applied Mathematics (ICNAAM2010)
  • Place of Presentation: Rhodes Palace Hotel, Rhodes, Greece
  • Year and Date: 2010-09-20
• [Presentation] 芝生の造成における競争種の共存モデル (2010)
  • Author(s): 江崎信行・三井斌友
  • Organizer: 日本応用数理学会2010年度年会
  • Place of Presentation: 明治大学駿河台校舎(東京)
  • Year and Date: 2010-09-08
• [Presentation] Two-step family of "look-ahead" linear multistep methods for ODEs (2010)
  • Author(s): T. Mitsui, D. Yakubu
  • Organizer: 日本応用数理学会2010年度年会
  • Place of Presentation: 明治大学駿河台校舎
  • Year and Date: 2010-09-06
• [Presentation] Two-step family of "look-ahead" linear multistep methods for ODEs (2010)
  • Author(s): T.Mitsui, D.Yakubu
  • Organizer: 日本応用数理学会2010年度年会
  • Place of Presentation: 明治大学駿河台校舎(東京)
  • Year and Date: 2010-09-06
• [Presentation] 芝草の成長過程を表わすlogistic方程式とその数値解 (2009)
  • Author(s): 江崎信行・三井斌友・小藤俊幸
  • Organizer: 日本応用数理学会2009年度年会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-28
• [Presentation] 芝草の成長過程を表わす logistic 方程式とその数値解 (2009)
  • Author(s): 江崎信行・三井斌友・小藤俊幸
  • Organizer: 日本応用数理学会2009年度年会
  • Place of Presentation: 大阪大学豊中キャンパス(豊中市)
  • Year and Date: 2009-09-28
• [Presentation] Look-ahead linear multistep methods (2009)
  • Author(s): T. Mitsui, D. Yakubu
  • Organizer: 12th Seminar on Numerical Solution of Differential and Differential-Algebraic Equations
  • Place of Presentation: Univ. of Halle, Halle, Germany
  • Year and Date: 2009-09-15
• [Presentation] "Look-ahead" linear multistep methods (2009)
  • Author(s): T.Mitsui, D.Yakubu
  • Organizer: 12th Seminar on Numerical Solution of Differential and Differential-Algebraic Equations
  • Place of Presentation: Halle, Germany
  • Year and Date: 2009-09-15
• [Presentation] Numerical modeling for growth of lawn grasses and its computational solution (2009)
  • Author(s): N. Esaki, T. Mitsui, et al.
  • Organizer: 2009 International Conference on Scientific Computation and Differential Equations(SciCADE09)
  • Place of Presentation: 北京,中国
  • Year and Date: 2009-05-29
• [Presentation] Numerical modeling for growth of lawn grasses and its computational solution (2009)
  • Author(s): N.Esaki, T.Mitsui, et al.
  • Organizer: 2009 International Conference on Scientific Computation and Differential Equations(SciCADE09)
  • Place of Presentation: Beijing, China
  • Year and Date: 2009-05-29