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Development of super high-efficient methods for equations with singularity and their theoretical supports

Research Project

Project/Area Number 24760060
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Engineering fundamentals
Research InstitutionHiroshima City University (2014-2016)
Hitotsubashi University (2012-2013)

Principal Investigator

Okayama Tomoaki  広島市立大学, 情報科学研究科, 講師 (80587866)

Project Period (FY) 2012-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords数値解析
Outline of Final Research Achievements

Differential equations and integral equations with singularities often arise in physics and chemistry, but numerical simulation of those equations is difficult by means of existing general numerical methods. For such equations, existing methods cannot achieve their usual performance, and there is no theoretical support of convergence to the solution. This study developed a highly efficient numerical method based on the Sinc numerical methods, which are robust and efficient for singularities. This study also gave theoretical support of the proposed method.

Report

(6 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (47 results)

All 2017 2016 2015 2014 2013 2012 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results,  Open Access: 5 results,  Acknowledgement Compliant: 5 results) Presentation (29 results) (of which Int'l Joint Research: 8 results,  Invited: 4 results)

  • [Journal Article] A Function Approximation Formula Using the Ganelius Sampling Points2017

    • Author(s)
      鵜島崇, 田中健一郎, 岡山友昭, 杉原正顯
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics

      Volume: 27 Issue: 1 Pages: 1-20

    • DOI

      10.11540/jsiamt.27.1_1

    • NAID

      130007043633

    • ISSN
      2424-0982
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces2017

    • Author(s)
      Ken'ichiro Tanaka, Tomoaki Okayama and Masaaki Sugihara
    • Journal Title

      IMA Journal of Numerical Analysis

      Volume: 37 Pages: 861-904

    • DOI

      10.1093/imanum/drw022

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Error estimates with explicit constants for the Sinc approximation over infinite intervals2017

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      Applied Mathematics and Computation

      Volume: 印刷中 Pages: 125-137

    • DOI

      10.1016/j.amc.2017.02.022

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Error estimate with explicit constants for the trapezoidal formula combined with Muhammad-Mori's SE transformation for the semi-infinite interval2017

    • Author(s)
      Tomoaki Okayama and Koichi Machida
    • Journal Title

      JSIAM Letters

      Volume: 印刷中

    • NAID

      130005681235

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Potential theoretic approach to design of accurate numerical integration formulas in weighted Hardy spaces2017

    • Author(s)
      Ken'ichiro Tanaka, Tomoaki Okayama and Masaaki Sugihara
    • Journal Title

      Approximation Theory XV: San Antonio 2016

      Volume: -

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Explicit error bound for modified numerical iterated integration by means of Sinc methods2016

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9582 Pages: 202-217

    • DOI

      10.1007/978-3-319-32859-1_17

    • ISBN
      9783319328584, 9783319328591
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Verified Error Bounds for the Real Gamma Function using Double Exponential Formula over Semi-Infinite Interval2016

    • Author(s)
      Naoya Yamanaka, Tomoaki Okayama, Shin'ichi Oishi
    • Journal Title

      Mathematical Aspects of Computer and Information Sciences

      Volume: 9582 Pages: 224-228

    • DOI

      10.1007/978-3-319-32859-1_19

    • ISBN
      9783319328584, 9783319328591
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical analysis of Sinc-Nystroem methods for Volterra integral equations2015

    • Author(s)
      Tomoaki Okayama, Takayasu Matsuo and Masaaki Sugihara
    • Journal Title

      Mathematics of Computation

      Volume: 84 Issue: 293 Pages: 1189-1215

    • DOI

      10.1090/s0025-5718-2014-02929-3

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Improvement of a Sinc-collocation method for Fredholm integro-differential equations2015

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      AIP Conference Proceedings

      Volume: 1648 Pages: 390008-390008

    • DOI

      10.1063/1.4912618

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 第二種積分方程式に対するSinc選点法の改良とその理論解析2014

    • Author(s)
      岡山友昭
    • Journal Title

      応用数理

      Volume: 24 Pages: 14-18

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] High-precision eigenvalue bound for the Laplacian with singularities2014

    • Author(s)
      Xuefeng Liu, Tomoaki Okayama and Shin'ichi Oishi
    • Journal Title

      Computer Mathematics

      Volume: Part III Pages: 311-323

    • DOI

      10.1007/978-3-662-43799-5_23

    • ISBN
      9783662437988, 9783662437995
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Explicit error bound for the tanh rule and the DE formula for integrals with logarithmic singularity2014

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 9-11

    • DOI

      10.14495/jsiaml.6.9

    • NAID

      130003394982

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Error estimates with explicit constants for Sinc quadrature and Sinc indefinite integration over infinite intervals2013

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      Reliable Computing

      Volume: 19

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on the Sinc approximation with boundary treatment2013

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      JSIAM Letters

      Volume: 5

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration2013

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      Numerische Mathematik

      Volume: in press Issue: 2 Pages: 361-394

    • DOI

      10.1007/s00211-013-0515-y

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods. Part I: Definite integration and function approximation2013

    • Author(s)
      Tomoaki Okayama
    • Journal Title

      Numerische Mathematik

      Volume: in press Issue: 3 Pages: 511-543

    • DOI

      10.1007/s00211-013-0540-x

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods. Part II: Indefinite integration2013

    • Author(s)
      Ken'ichiro Tanaka
    • Journal Title

      Numerische Mathematik

      Volume: in press Issue: 3 Pages: 545-568

    • DOI

      10.1007/s00211-013-0541-9

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 第二種積分方程式に対するSinc法の実用的視点からの理論解析2012

    • Author(s)
      岡山友昭
    • Journal Title

      日本応用数理学会論文誌

      Volume: 22

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Recent development of variable transformations combined with the trapezoidal formula2017

    • Author(s)
      Tomoaki Okayama
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017
    • Place of Presentation
      Hotel Breeze Bay Marina (Miyakojima, Okinawa)
    • Year and Date
      2017-03-18
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Verified error bounds for the modified Bessel function of the second kind using double exponential formula over semi-infinite interval2017

    • Author(s)
      Naoya Yamanaka, Tomoaki Okayama and Shin'ichi Oishi
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017
    • Place of Presentation
      Hotel Breeze Bay Marina (Miyakojima, Okinawa)
    • Year and Date
      2017-03-18
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Muhammad-MoriのSE-Sinc不定積分公式に対する定数を明示的に表した誤差評価2017

    • Author(s)
      原涼太, 岡山友昭
    • Organizer
      日本応用数理学会2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2017-03-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] Sinc関数近似に用いる半無限区間用SE変換の改善と理論誤差評価2017

    • Author(s)
      新宅勇也, 桂浦英佑, 岡山友昭
    • Organizer
      日本応用数理学会2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2017-03-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] eye-shaped領域上の重み付きハーディ空間における2つの最適な関数近似公式の比較2016

    • Author(s)
      杉田幸亮, 杉原正顯, 田中健一郎, 岡山友昭
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] 重み付きハーディ空間における高精度数値積分公式の設計2016

    • Author(s)
      田中健一郎, 岡山友昭, 杉原正顯
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] Potential theoretic approach to approximation in weighted Hardy spaces2016

    • Author(s)
      Ken'ichiro Tanaka, Tomoaki Okayama and Masaaki Sugihara
    • Organizer
      The 11th East Asia SIAM Conference
    • Place of Presentation
      University of Macau (China)
    • Year and Date
      2016-06-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error estimates with explicit constants for the Sinc approximation over infinite intervals2016

    • Author(s)
      Tomoaki Okayama
    • Organizer
      5th European Seminar on Computing
    • Place of Presentation
      Pilsner Urquell Brewery (Czech Republic)
    • Year and Date
      2016-06-09
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified algorithm for the modified Bessel function of the second kind2016

    • Author(s)
      Naoya Yamanaka, Tomoaki Okayama, Shin'ichi Oishi and Yukari Maki
    • Organizer
      5th European Seminar on Computing
    • Place of Presentation
      Pilsner Urquell Brewery (Czech Republic)
    • Year and Date
      2016-06-09
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] DE公式を用いた変形Bessel関数の精度保証付き数値計算2016

    • Author(s)
      山中脩也, 岡山友昭, 大石進一, 槙友佳里
    • Organizer
      日本応用数理学会2016年研究部会連合発表会
    • Place of Presentation
      神戸学院大学ポートアイランドキャンパス
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report
  • [Presentation] Verified error bounds for the real gamma function using double exponential formula over semi-infinite interval2015

    • Author(s)
      Naoya Yamanaka, Tomoaki Okayama, and Shin'ichi Oishi
    • Organizer
      6th International Conference on Mathematical Aspects of Computer and Information Sciences
    • Place of Presentation
      Zuse Institute Berlin
    • Year and Date
      2015-11-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Explicit error bound for modified numerical iterated integration by means of Sinc methods2015

    • Author(s)
      Tomoaki Okayama
    • Organizer
      6th International Conference on Mathematical Aspects of Computer and Information Sciences
    • Place of Presentation
      Zuse Institute Berlin
    • Year and Date
      2015-11-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 無限区間二次元積分に対する極座標変換とDE変換を用いた複合台形則の適用への注意2015

    • Author(s)
      岡山友昭, 小城雄輝
    • Organizer
      日本応用数理学会2015年度年会
    • Place of Presentation
      金沢大学角間キャンパス
    • Year and Date
      2015-09-11
    • Related Report
      2015 Research-status Report
  • [Presentation] Potential theoretic approach to design an optimal formula for function approximation in a weighted Hardy space2015

    • Author(s)
      Ken'ichiro Tanaka, Tomoaki Okayama, Masaaki Sugihara
    • Organizer
      New Directions in Numerical Computation
    • Place of Presentation
      Oxford University
    • Year and Date
      2015-08-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] ポテンシャル論による重み付きハーディ空間上の最適関数近似公式の設計2015

    • Author(s)
      田中健一郎, 岡山友昭, 杉原正顯
    • Organizer
      第44回数値解析シンポジウム
    • Place of Presentation
      山梨県甲州市
    • Year and Date
      2015-06-08
    • Related Report
      2015 Research-status Report
  • [Presentation] Muhammad-MoriのSE公式に対する定数を明示的に表した誤差評価2015

    • Author(s)
      岡山友昭, 町田洸一
    • Organizer
      日本応用数理学会2015年研究部会連合発表会
    • Place of Presentation
      明治大学中野キャンパス
    • Year and Date
      2015-03-07
    • Related Report
      2014 Research-status Report
  • [Presentation] Improvement of a Sinc-collocation method for Fredholm integro-differential equations2014

    • Author(s)
      Tomoaki Okayama
    • Organizer
      12th International Conference of Numerical Analysis and Applied Mathematics
    • Place of Presentation
      Rodos Palace Hotel
    • Year and Date
      2014-09-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Theoretical analysis of a Sinc-Nystroem method for Volterra integro-differential equations and its improvement

    • Author(s)
      Tomoaki Okayama
    • Organizer
      18th International Conference Mathematical Modelling and Analysis (MMA2013) and Fourth International Conference Approximation Methods and Orthogonal Expansions (AMOE2013)
    • Place of Presentation
      Dorpat Conference Centre (Tartu, Tartu County, Estonia)
    • Related Report
      2013 Research-status Report
  • [Presentation] Fredholm微積分方程式に対するSinc-Nystroem法とその理論解析

    • Author(s)
      岡山友昭
    • Organizer
      第42回数値解析シンポジウム
    • Place of Presentation
      四国道後舘(愛媛県松山市)
    • Related Report
      2013 Research-status Report
  • [Presentation] SE-Sinc法が有効な関数族に対するDE-Sinc法の収束性について

    • Author(s)
      岡山友昭
    • Organizer
      日本応用数理学会2012年度年会
    • Place of Presentation
      アクロス福岡(福岡県福岡市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Sinc-collocation methods for Volterra integro-differential equations

    • Author(s)
      Tomoaki Okayama
    • Organizer
      International Conference on Scientific Computation and Differential Equations 2013 (SciCADE 2013)
    • Place of Presentation
      University of Valladolid (Valladolid, Castile and Leon, Spain)
    • Related Report
      2013 Research-status Report
  • [Presentation] 第二種Fredholm積分方程式に対するSinc選点法の事後誤差評価

    • Author(s)
      岡山友昭
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス(滋賀県大津市)
    • Related Report
      2013 Research-status Report
  • [Presentation] 非整数階微分方程式の初期値問題に対するSinc選点法

    • Author(s)
      岡山友昭
    • Organizer
      第41回数値解析シンポジウム
    • Place of Presentation
      群馬県渋川市
    • Related Report
      2012 Research-status Report
  • [Presentation] Sinc-collocation method for initial value problems by means of the DE transformation

    • Author(s)
      Tomoaki Okayama
    • Organizer
      The 16th International Congress on Computational and Applied Mathematics
    • Place of Presentation
      Ghent University (Ghent, East Flanders, Belgium)
    • Related Report
      2012 Research-status Report
  • [Presentation] 無限区間のSinc関数近似に対する定数を明示的に表した誤差評価

    • Author(s)
      岡山友昭
    • Organizer
      日本応用数理学会2012年度年会
    • Place of Presentation
      北海道稚内市
    • Related Report
      2012 Research-status Report
  • [Presentation] Error estimates with explicit constants for Sinc quadrature and Sinc indefinite integration over infinite intervals

    • Author(s)
      Tomoaki Okayama
    • Organizer
      The 15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
    • Place of Presentation
      Akademgorodok, Novosibirsk, Russia
    • Related Report
      2012 Research-status Report
  • [Presentation] Sinc積分とSinc不定積分による累次積分近似に対する定数を明示的に表した誤差評価

    • Author(s)
      岡山友昭
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス(滋賀県大津市)
    • Related Report
      2012 Research-status Report
  • [Presentation] 二重指数関数型数値積分公式の誤差の見積もりについて

    • Author(s)
      岡山友昭
    • Organizer
      日本応用数理学会三部会連携「応用数理セミナー」
    • Place of Presentation
      東京大学本郷キャンパス(東京都文京区)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 対数的特異性をもつ積分に対するtanh則・DE公式の定数を明示的に表した誤差評価

    • Author(s)
      岡山友昭
    • Organizer
      日本応用数理学会2013年研究部会連合発表会
    • Place of Presentation
      東洋大学白山キャンパス(東京都文京区)
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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