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Research and Development of Numerical Analysis Software

Research Project

Project/Area Number 02640173
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHiroshima University

Principal Investigator

SHINTANI H.  Hiroshima Univ. Fac. of School. Education, Prof., 学校教育学部, 教授 (90033802)

Co-Investigator(Kenkyū-buntansha) KAGEYAMA S.  Hiroshima Univ. Fac. of School Education, Ass. Prof., 学校教育学部, 助教授 (70033892)
IKEDA A.  Hiroshima Univ. Fac. of School Education, Ass. Prof., 学校教育学部, 助教授 (30093363)
OKADA Y.  Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (70093739)
ISHIBASHI Y.  Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (30033848)
YAMAGUTI K.  Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (20040090)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1991: ¥100,000 (Direct Cost: ¥100,000)
Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000)
KeywordsNumerical analysis software / Numerical methods for differential equation / Numerical methods for algebraic equations / Mathematics education software / 数値解析ソフトウエア / 数学教育ソフトウエア
Research Abstract

Methods for numerical solution of initial value problem for systems of stiff ordinary differential equations are studied. Existence of 5-stage singley diagonally implicit one-step methods of order 5 is proved. Starters for numerical solution methods are obtained for a singular systems of differential equations of the second order. It has been shown that there exist two-step methods of order 4, 5 and 6 which enable us to estimate the local error and to interpolate at nonstep points and that there exist such methods with one off-step point of order 5, 6 and 7.
The behavior of solution curves of nonlinear systems in the neighborhood of a nonsimple bifurcation point is studied in detail. Methods for constructing extended systems to determine double and triple turning points are developed.
Characterization of semi-regular and regular experimental designs is given and nonexistence of a certain kind of design is proved.
A personal computer program is written for diagnosing the ability of adding two integers of two figures.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Hisayoshi SHINTANI: "Existence of 5ーStage Singley Diagonally Implicit OneーStep" 広島大学学校教育学部紀要第II部. 13. 29-34 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Hisayoshi SHINTANI: "Starting Methods for Numerical Solution of a Singular Systems of Ordinary Differential Equations of the Second Order" 広島大学学校教育学部紀要第II部. 13. 21-2l (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Hisayoshi SHINTANI: "VariableーStep Embedded TwoーStep Methods with Interpolants" 広島大学学校教育学部紀要第II部. 14. 53-59 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Hisayoshi SHINTANI: "Nonsimple Bifurcation Points and Perturbations" 広島大学学校教育学部紀要第II部. 14. 61-72 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Sanpei KAGEYAMA: "On Two Efficiency Factors of a Proper Block Designs" 広島大学学校教育学部紀要第II部. 14. 33-37 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Sanpei KAGEYAMA: "Some Characterizations of Semiーregular and Regular Designs" 広島大学学校教育学部紀要第II部. 14. 39-52 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SHINTANI, H.: "Starting Methods for Numerical Solution of a Singular System of Ordinary Differential Equations of the Second Order" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 13. 21-28 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SHINTANI, H.: "Existence of 5-Stage Singly Diagonally Implicit One-Step Methods of Order 5" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 13. 29-34 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SHINTANI, H.: "Variable-Step Embedded Two-Step Methods with Interpolants" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 14. 53-59 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SHINTANI, H.: "Nonsimple bifurcation points and Perturbations" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 14. 61-72 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KAGEYAMA, S.: "On Two Efficiency Factors of a Proper Block Designs" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 14. 33-37 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KAGEYAMA, S.: "Some Characterizations of Semi-Regular and Regular Designs" Bull. of Fac. School. Educ., Hiroshima Univ.Part II 14. 39-52 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Hisayoshi SHINTANI: "VariableーStep Embedded TwoーStep Methods with Interpolants" 広島大学学校教育学部紀要 第II部. 14. 53-59 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hisayoshi SHINTANI: "Nonsimple Bifurcation Points and Perturbations" 広島大学学校教育学部紀要 第II部. 14. 61-72 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Sanpei KAGEYAMA: "On Two Efficiency Factors of a Proper Block Designs" 広島大学学校教育学部紀要 第II部. 14. 33-37 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Sanpei KAGAYAMA: "Some Characterizations of Semiーregular and Regular Designs" 広島大学学校教育学部紀要 第II部. 14. 39-52 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Yasunori ISHIBASHI: "Note on Differential Operator X_1+X_2+・・・・+X_n=0" 広島大学学校教育学部紀要 第II部. 14. 29-31 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hisayoshi SHINTANI: "Existence of 5ーStage Singley Diagonally Implicit OneーSteP Methods of Order 5" 広島大学学校教育学部紀要第II部. 13. 29-34 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Hisayoshi SHINTANI: "Starting Methods for Numerical Solution of a Singular System of Ordinary Differential Equations of the Second Order" 広島大学学校教育学部紀要第II部. 13. 21-26 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Kiyoshi YAMAGUTI: "Arithmetic and Mathematics from Viewpoint of Tripleness" 広島大学学校教育学部紀要第II部. 13. 35-47 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Yasunori ISHIVASHI: "Note on Rings of Invariants Associated with μpーActions" 広島大学学校教育学部紀要第II部. 13. 11-15 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Akira IKEDA: "Zeta Functions for Differential Froms on Complex Projective Spaces and Their Asymptotic Expansions" 広島大学学校教育学部紀要第II部. 13. 1-9 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Sanpei KAGEYAMA: "A Characterization of Generalized Binary Proper EffciencyーBalanced Designs" 広島大学学校教育学部紀要第II部. 13. 17-20 (1991)

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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