Updated on 2022/09/28

写真a

 
TANAKA, Kazuaki
 
Affiliation
Faculty of Science and Engineering, Waseda Research Institute for Science and Engineering
Job title
Junior Researcher(Assistant Professor)

Concurrent Post

  • Faculty of Science and Engineering   School of Fundamental Science and Engineering

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Education

  • 2014.04
    -
    2017.03

    Waseda University   Graduate School of Fundamental Science and Engineering (Doctor course)  

  • 2012.04
    -
    2014.03

    Waseda University   Graduate School of Fundamental Science and Engineering (Master course)  

  • 2008.04
    -
    2012.03

    Waseda University   School of Fundamental Science and Engineering   Department of Applied Mathematics  

Degree

  • 早稲田大学   博士(工学)

Research Experience

  • 2018.04
    -
    Now

    Waseda University   Research Institute for Science and Engineering

  • 2017.04
    -
    2018.03

    Waseda University   Faculty of Science and Engineering

Professional Memberships

  •  
     
     

    日本数学会

  •  
     
     

    日本応用数理学会

 

Research Areas

  • Basic mathematics

  • Applied mathematics and statistics

Research Interests

  • 計算機援用証明

  • 精度保証付き数値計算

  • 数値解析

  • 偏微分方程式

Papers

  • Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents

    Kazuaki Tanaka, Michael Plum, Kouta Sekine, Masahide Kashiwagi, Shin'ichi Oishi

    Numerical Functional Analysis and Optimization   43 ( 3 ) 322 - 349  2022.04  [Refereed]

    Authorship:Lead author

    DOI

  • A posteriori verification of the positivity of solutions to elliptic boundary value problems

    Kazuaki Tanaka, Taisei Asai

    Partial Differential Equations and Application    2022.03  [Refereed]

    Authorship:Lead author

    DOI

  • Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems

    Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi

    Computers & Mathematics with Applications   106   18 - 26  2022.01  [Refereed]

    DOI

  • Numerical verification for asymmetric solutions of the Hénon equation on bounded domains

    Taisei Asai, Kazuaki Tanaka, Shin’ichi Oishi

    Journal of Computational and Applied Mathematics     113708 - 113708  2021.07  [Refereed]

    DOI

  • A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations

    Kazuaki Tanaka

    Japan Journal of Industrial and Applied Mathematics    2021.01  [Refereed]

    Authorship:Lead author

     View Summary

    <title>Abstract</title>This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary conditions: Dirichlet, Neumann, and mixed. Given explicitly estimated error bounds between an exact solution <italic>u</italic> and a numerically computed approximate solution <inline-formula><alternatives><tex-math>$${\hat{u } }$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
    <mml:mover>
    <mml:mi>u</mml:mi>
    <mml:mo>^</mml:mo>
    </mml:mover>
    </mml:math></alternatives></inline-formula>, we evaluate the number of sign-changes of <italic>u</italic> (the number of nodal domains) and determine the location of zero level-sets of <italic>u</italic> (the location of the nodal line). We apply this method to the Dirichlet problem of the Allen–Cahn equation. The nodal line of solutions of this equation represents the interface between two coexisting phases.

    DOI

  • Numerical verification method for positive solutions of elliptic problems

    Kazuaki Tanaka

    Journal of Computational and Applied Mathematics   370   112647 - 112647  2020.05  [Refereed]

    Authorship:Lead author

    DOI

  • Numerical verification for positive solutions of Allen–Cahn equation using sub- and super-solution method

    Yuta Matsushima, Kazuaki Tanaka, Shin’ichi Oishi

    Journal of Advanced Simulation in Science and Engineering   7 ( 1 ) 136 - 150  2020  [Refereed]

    DOI

  • 半線形楕円型境界値問題の精度保証付き数値計算結果の改善

    酒井将大, 田中一成, 大石進一

    日本応用数理学会論文誌   29 ( 1 ) 17 - 45  2019.03  [Refereed]

  • Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

    Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   299   1 - 18  2017.11  [Refereed]

     View Summary

    This paper is concerned with an explicit value of the embedding constant from W-1,W- q(Omega) to L-p(Omega) for a domain Omega subset of R-N (N is an element of N), where 1 &lt;= q &lt;= p &lt;=infinity. We previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by estimating the norm of Stein's extension operator. Although this formula can be applied to a domain Omega that can be divided into a finite number of Lipschitz domains, there was room for improvement in terms of accuracy. In this paper, we report that the accuracy of the embedding constant is significantly improved by restricting Omega to a domain dividable into bounded convex domains.

    DOI

  • Numerical validation of blow-up solutions of ordinary differential equations

    Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   314   10 - 29  2017.04  [Refereed]

     View Summary

    This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method. (C) 2016 Elsevier B.V. All rights reserved.

    DOI

  • Sharp numerical inclusion of the best constant for embedding H-0(1)(Omega) hooked right arrow L-p (Omega) on bounded convex domain

    Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   311   306 - 313  2017.02  [Refereed]

     View Summary

    In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H-0(1)(Omega) hooked right arrow L-p (Omega) on a bounded convex domain in R-2. We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented. (C) 2016 Elsevier B.V. All rights reserved.

    DOI

  • Numerical verification method for positivity of solutions to elliptic equations

    Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi

    RIMS Kokyuroku No.2037, Numerical Analysis: New Developments for Elucidating Interdisciplinary Problems II   ( 2037 ) 125 - 140  2017

     View Summary

    In this paper, we propose a numerical method for verifying the positivity of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the equation, which can be checked numerically without requiring a complicated computation. We present some numerical examples.

    CiNii

  • Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator

    Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   389  2015.12  [Refereed]

     View Summary

    In this paper, we propose a method for estimating the Sobolev-type embedding constant from W-1,W-q(Omega) to L-p(Omega) on a domain Omega subset of R-n (n = 2,3, ... ) with minimally smooth boundary (also known as a Lipschitz domain), where p is an element of(n/(n - 1), infinity) and q = np/(n + p). We estimate the embedding constant by constructing an extension operator from W-1,W-q(Omega) to W-1,W-q(R-n) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.

    DOI

  • Numerical verification of positiveness for solutions to semilinear elliptic problems

    Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

    JSIAM Letters   7   73 - 76  2015  [Refereed]

    DOI

  • Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation

    Kazuaki Tanaka, Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   31 ( 3 ) 665 - 679  2014.11  [Refereed]

     View Summary

    This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computations of solutions to elliptic boundary value problems. The proposed method uses a generalized eigenvalue problem to derive the norm estimation. This method has several advantages. Namely, it can be applied to two types of boundary conditions: the Dirichlet type and the Neumann type. It also provides a way of numerically evaluating lower and upper bounds of target eigenvalues. Numerical examples are presented to show that the proposed method provides effective estimations in most cases.

    DOI

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Awards

  • 船井研究奨励賞

    2022.05   公益財団法人船井情報科学振興財団  

  • 第8回WASEDA e-Teaching Award 大賞

    2020.03  

  • 2016年度大川功記念特別優秀賞

    2016  

    Winner: 田中一成

  • 優秀ポスター賞

    2016   日本応用数理学会2016年度年会  

    Winner: 若山馨太, 田中一成, 関根晃太, 尾崎克久, 大石進一

  • Student Presentation Award

    2014   JSST 2014 International Conference  

    Winner: Kazuaki Tanaka

  • Student Presentation Award

    2013   JSST 2013 International Conference  

    Winner: Kazuaki Tanaka

▼display all

Research Projects

  • 精度保証付きニューラルネットワーク数値計算理論の確立

    科学技術振興機構 (JST)  創発的研究支援事業

    Project Year :

    2021.04
    -
    2028.03
     

    田中一成

  • 精度保証付き数値計算による反応拡散モデルの解に対する符号変化構造解析

    日本学術振興会  科学研究費助成事業 若手研究

    Project Year :

    2019.04
    -
    2022.03
     

    田中 一成

  • 相分離現象解明のための精度保証付き数値計算法

    公益財団法人 大川情報通信基金  公益財団法人 大川情報通信基金 2020年度 研究助成

    Project Year :

    2021.01
    -
    2021.12
     

    田中一成

  • 反応拡散モデルを記述する偏微分方程式の正値解に対する精度保証付き数値計算法と関連する数学上の問題に関する研究

    Mizuho Foundation for the Promotion of Sciences 

    Project Year :

    2017.04
    -
    2020.03
     

  • Verified numerical computation for solutions to partial differential equations describing reaction diffusion models

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity start-up

    Project Year :

    2017.08
    -
    2019.03
     

    TANAKA Kazuaki

     View Summary

    This study developed verified numerical computation methods for the following reaction diffusion model
    ∂u/∂t(t,x) = △u(t,x)+f(x,u(t,x)), t∈(0,∞), x∈Ω (1).
    More precisely,the study, especially focusing on the stationary problem with respect to (1), developed a numerical method of enclosing positive solutions in the strict mathematical sense. The method ensures the existence of an exact solution of (1) nearby its numerical approximation with strict error bounds,at the same time guaranteeing the positively of the exact solution in the strict mathematical sense.

Presentations

  • エノン方程式の解に対する正値性検証法

    田中一成  [Invited]

    精度保証付き数値計算の実問題への応用研究集会 (NVR 2020) 

    Presentation date: 2020.11

  • 精度保証付き数値計算を用いたHénon方程式の対称性に関する考察

    浅井大晴, 田中一成, 大石進一  [Invited]

    精度保証付き数値計算の実問題への応用研究集会 (NVR 2020) 

    Presentation date: 2020.11

  • 楕円型境界値問題に対する解符号の事後検証法

    田中一成, 浅井大晴

    日本応用数理学会2020年度年会 

    Presentation date: 2020.09

  • 精度保証付き数値計算を用いたHenon方程式の多重解の存在証明

    浅井大晴, 田中一成, 大石進一

    日本応用数理学会2020年度年会 

    Presentation date: 2020.09

  • A priori error estimates for Poisson's equation with discontinuous coefficients

    田中一成, 中尾充宏

    日本応用数理学会2019年度連合発表会 

    Event date:
    2020.03
     
     
  • 優解劣解法を用いた Allen-Cahn 方程式の正値解に対する精度保証付き数値計算

    松嶋佑汰, 田中一成, 大石進一

    2019年度応用数学合同研究集会 

    Presentation date: 2019.12

  • 精度保証付き数値計算を用いた Henon 方程式の非対称解の存在証明

    浅井大晴, 田中一成, 大石進一

    2019年度応用数学合同研究集会 

    Presentation date: 2019.12

  • Numerical verification for positive global-in-time solutions of Allen-Cahn equation in three space dimensions using sub- and super-solution method

    Yuta Matsushima, Kazuaki Tanaka, Shin’ichi Oishi

    The 38th JSST Annual International Conference on Simulation Technology 

    Presentation date: 2019.11

  • Numerical verification for asymmetric solutions of the Henon equation

    Taisei Asai, Kazuaki Tanaka, Shin’ichi Oishi

    The 38th JSST Annual International Conference on Simulation Technology 

    Presentation date: 2019.11

  • 楕円型方程式の弱解に対する正値性証明法

    田中一成

    日本応用数理学会2019年度年会 

    Event date:
    2019.09
     
     
  • 空間3次元Allen-Cahn方程式の正値時間大域解に対する精度保証付き数値計算法

    松嶋佑汰, 田中一成, 大石進一

    日本応用数理学会2019年度年会 

    Event date:
    2019.09
     
     
  • Henon方程式の非対称解に対する精度保証付き数値計算

    浅井大晴, 田中一成, 大石進一

    日本応用数理学会2019年度年会 

    Event date:
    2019.09
     
     
  • Rigorous solution-enclosures of elliptic problems and its application to the best embedding constants, Minisymposium "Numerical verification methods and their application to differential equations"

    Kazuaki Tanaka, Kouta Sekine

    9th International Congress on Industrial and Applied Mathematics - ICIAM 2019 

    Presentation date: 2019.07

  • 精度保証付き数値計算を用いた楕円型境界値問題の解の符号変化構造解析

    田中一成

    数学と諸分野の連携にむけた若手数学者交流会 

    Presentation date: 2019.03

  • Estimation of Sobolev embedding constant on a bounded convex domain

    Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine, Shin’ichi Oishi

    The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN2018) 

    Presentation date: 2018.09

  • Numerical verification method for positive solutions of Allen-Cahn equation using sub- and super-solution method

    Yuta Matsushima, Kazuaki Tanaka, Shin’ichi Oishi

    The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN2018)  (Waseda University, Tokyo, Japan) 

    Presentation date: 2018.09

  • Numerical verification method for elliptic problems with sign change information

    Kazuaki Tanaka, Kazunaga Tanaka

    The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN2018)  (Waseda University, Tokyo, Japan) 

    Presentation date: 2018.09

  • 優解劣解法を用いたアレンカーン方程式の解の精度保証付き数値計算

    松嶋佑汰, 田中一成, 大石進一

    日本応用数理学会2017年度連合発表会  (大阪大学吹田キャンパス) 

    Presentation date: 2018.03

  • 半線形楕円型境界値問題の高エネルギー解に対する精度保証付き数値計算

    酒井将大, 田中一成, 大石進一

    日本応用数理学会2017年度連合発表会  (大阪大学吹田キャンパス) 

    Presentation date: 2018.03

  • アレン・カーン方程式の解に対する精度保証付き数値計算

    田中一成

    CREST・さきがけ数学関連領域合同シンポジウム −数学パワーが世界を変える2018−  (富士ソフト秋葉原ビル5Fアキバホール) 

    Presentation date: 2018.01

  • 前処理ソート付き逐次添加法によるドロネー性保証付き三角形分割法

    若山馨太, 金子直樹, 田中一成, 関根晃太, 尾崎克久, 大石進一

    日本応用数理学会2017年度年会  (武蔵野大学 有明キャンパス) 

    Presentation date: 2017.09

  • Computer assisted analysis of stationary problem of Allen-Cahn equation

    Shin'ichi Oishi, Kazuaki Tanaka

    International Workshop on Industrial Mathematics 2017  (Burjassot (Valencia)) 

    Presentation date: 2017.05

  • 線形化問題の精度保証を利用した非線形楕円型境界値問題の精度保証結果の改善

    酒井将大, 田中一成, 大石進一

    日本応用数理学会2016年度連合発表会  (電気通信大学) 

    Presentation date: 2017.03

  • Numerical method for estimating the best constant in Sobolev type inequality on unit square

    Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

    The International Workshop on Numerical Verification and its Applications  (Miyakojima-island, Okinawa, Japan,) 

    Presentation date: 2017.03

  • Verified numerical computation for stationary problem of Allen-Cahn equation

    Shin'ichi Oishi, Kazuaki Tanaka

    The 53rd meeting of ANXIAM 2017  (Hahndorf, South Australia) 

    Presentation date: 2017.02

  • 精度保証付きドロネー三角形分割の計算手法に対する考察

    若山馨太, 田中一成, 関根晃太, 尾崎克久, 大石進一

    数学・数理科学専攻若手研究者のための異分野・異業種研究交流会2016  (明治大学中野キャンパス) 

    Presentation date: 2016.11

  • 有界な凸領域における連立楕円型偏微分方程式の解の計算機援用存在証明法

    関根晃太, 田中一成, 大石進一  [Invited]

    The Twenty-Eighth RAMP Symposium 

    Presentation date: 2016.10

  • ある無限次元固有値を用いた楕円型偏微分方程式の解の存在性に対する計算機援用証明法

    関根晃太, 田中一成, 大石進一  [Invited]

    RIMS研究集会「現象解明に向けた数値解析学の新展開II」 

    Presentation date: 2016.10

  • 楕円型微分方程式の正値解に対する精度保証付き数値計算法

    田中一成, 関根晃太, 大石進一  [Invited]

    RIMS研究集会「現象解明に向けた数値解析学の新展開II」 

    Presentation date: 2016.10

  • Delaunay三角形分割の精度保証付き数値計算手法に対する考察

    若山馨太, 田中一成, 関根晃太, 尾崎克久, 大石進一

    日本応用数理学会2016年度年会  (北九州国際会議場) 

    Presentation date: 2016.09

  • Verified numerical computations for blow-up solutions of ODEs

    Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin’ichi Oishi

    The 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics. (2016) 

    Presentation date: 2016.09

  • A norm estimation for an inverse of linear operator using a minimal eigenvalue

    Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi

    The 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics. (2016) 

    Presentation date: 2016.09

  • On verified numerical computation for positive solutions to elliptic boundary value problems

    Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi

    The 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics. (2016) 

    Presentation date: 2016.09

  • Rigorous numerical inclusions of positive solutions to elliptic problems

    Shin'ichi Oishi, Kazuaki Tanaka  [Invited]

    International Workshop on Enclosure Methods  (Freudenstadt, Germany) 

    Presentation date: 2016.09

  • On verified numerical computation for elliptic Dirichlet boundary value problems using sub- and super-solution method

    Kazuaki Tanaka, Shin'ichi Oishi

    The fifth Asian conference on Nonlinear Analysis and Optimization  (Toki Messe, Niigata, Japan) 

    Presentation date: 2016.08

  • Estimation for optimal constant satisfying an inequality for linear operator using minimal eigenvalue

    Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi

    The fifth Asian conference on Nonlinear Analysis and Optimization  (Toki Messe, Niigata, Japan) 

    Presentation date: 2016.08

  • Rigorous numerics of blowup solutions for ODEs

    Kaname Matsue, Akitoshi Takayasu, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin’ichi Oishi

    The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications 

    Presentation date: 2016.07

  • Numerically verifiable condition for positivity of solution to elliptic equation

    Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi

    The 11th East Asia SIAM 

    Presentation date: 2016.06

  • 放物面コンパクト化を用いる常微分方程式の爆発解の数値的検証法

    高安亮紀, 松江要, 佐々木多希子, 田中一成, 水口信, 大石進一

    日本応用数理学会2015年度連合発表会  (神戸学院大学ポートアイランドキャンパス) 

    Presentation date: 2016.03

  • 偏微分方程式の正値解に対する精度保証付き数値計算

    田中一成, 関根晃太, 大石進一

    第3回JST数学領域横断若手合宿  (ウェスティンホテル淡路) 

    Presentation date: 2016.02

  • Numerical verification for positiveness of solutions to self-adjoint elliptic problems

    Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

    JSST 2015 International Conference on Simulation Technology 

    Presentation date: 2015.10

  • 常微分方程式の爆発解に対する精度保証付き数値計算

    高安亮紀, 松江要, 佐々木多希子, 田中一成, 水口信, 大石進一

    日本応用数理学会2015年度年会  (金沢大学) 

    Presentation date: 2015.09

  • 楕円型偏微分方程式の解の正値性に対する数値的検証法

    田中一成, 関根晃太, 水口信, 大石進一

    日本応用数理学会2015年度年会  (金沢大学) 

    Presentation date: 2015.09

  • 逐次添加法による三角形分割のDelaunay 性に対する数値的検証法

    若山馨太, 田中一成, 関根晃太, 尾崎克久, 大石進一

    日本応用数理学会2015年度年会  (金沢大学) 

    Presentation date: 2015.09

  • Verified numerical enclosure of blow-up time for ODEs

    高安亮紀, 松江要, 佐々木多希子, 田中一成, 水口信, 大石進一

    日本数学会2015年度年会  (京都産業大学) 

    Presentation date: 2015.09

  • 同次Dirichlet境界条件における埋め込み定数の評価について

    田中一成

    第18会環瀬戸内ワークショップ 

    Presentation date: 2015.08

  • 常微分方程式の解の爆発時刻に対する精度保証付き数値計算

    高安亮紀, 松江要, 佐々木多希子, 田中一成, 水口信, 大石進一

    第44回数値解析シンポジウム  (ぶどうの丘, 山梨県甲州市) 

    Presentation date: 2015.06

  • ODEの爆発解に対する精度保証付き数値計算

    高安亮紀, 松江要, 佐々木多希子, 田中一成, 大石進一

    CRESTシンポジウム,精度保証付き数値計算の最近の展開  (北九州国際会議場) 

    Presentation date: 2015.03

  • 偏微分方程式の解の正値性に対する数値的検証法

    田中一成, 水口信, 関根晃太, 大石進一

    CRESTシンポジウム,精度保証付き数値計算の最近の展開  (北九州国際会議場) 

    Presentation date: 2015.03

  • シグマノルムを利用した精度保証付き数値計算法の連立楕円型偏微分方程式への応用

    関根晃太, 田中一成, 高安亮紀, 山崎憲

    第47回日本大学生産工学部学術講演会  (日本大学) 

    Presentation date: 2014.12

  • Computer-assisted analysis for solutions to nonlinear elliptic Neumann problems

    Kazuaki Tanaka, Shin'ichi Oishi

    JSST 2014 International Conference on Simulation Technology 

    Presentation date: 2014.10

  • 重み付きノルムによる特異摂動問題の精度保証付き数値計算結果の改善

    関根晃太, 田中一成, 高安亮紀, 大石進一

    日本応用数理学会2014年度年会  (政策研究大学院大学) 

    Presentation date: 2014.09

  • Numerical verification for periodic stationary solutions to the Allen-Cahn equation

    Kazuaki Tanaka, Shin'ichi Oishi

    The16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics(SCAN2014) 

    Presentation date: 2014.09

  • An a priori estimation of the Sobolev embedding constant and its application to numerical verification for solutions to PDEs

    田中一成, 水口信, 関根晃太, 大石進一

    第10回日本応用理学会研究部会連合発表会  (京都大学吉田キャンパス総合研究8号館,) 

    Presentation date: 2014.03

  • Numerical verification for stationary solutions to the Allen-Cahn equation

    Kazuaki Tanaka, Shin'ichi Oishi

    The International Workshop on Numerical Verification and its Applications  (Waseda Univ. Nishiwaseda campus, Japan,) 

    Presentation date: 2014.03

  • 線形楕円型作用素のNeumann条件下における精度保証付き逆作用素ノルム評価

    田中一成, 高安亮紀, 劉雪峰, 大石進一

    日本応用数理学会2013年度年会  (アクロス福岡, 福岡県福岡市) 

    Presentation date: 2013.09

  • Estimation of an embedding constant on Lipschitz domains using extension operators

    Kazuaki Tanaka, Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi

    JSST 2013 International Conference on Simulation Technology 

    Presentation date: 2013.09

  • Verified norm estimation for the inverse of linear elliptic operators and its application

    Kazuaki Tanaka, Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi

    The 9th East Asia SIAM 

    Presentation date: 2013.06

  • 逆作用素ノルム評価を用いた楕円型Neumann境界値問題の解に対する精度保証付き数値計算

    田中一成, 高安亮紀, 劉雪峰, 大石進一

    日本応用数理学会2013年度連合発表会  (東洋大学白山キャンパス) 

    Presentation date: 2013.03

  • 線形楕円型作用素のNeumann条件下における精度保証付き逆作用素ノルム評価

    田中一成, 高安亮紀, 劉雪峰, 大石進一

    日本応用数理学会2012年度年会  (稚内全日空ホテル, 北海道稚内市) 

    Presentation date: 2012.08

  • ある固有値評価を利用した線形楕円型作用素の逆作用素に対する精度保証付きノルム評価

    田中一成, 高安亮紀, 大石進一

    第41回数値解析シンポジウム  (伊香保温泉よろこびの宿しん喜, 群馬県渋川市伊香保町) 

    Presentation date: 2012.06

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Specific Research

  • 反応拡散モデルを記述する偏微分方程式の正値解に対する精度保証付き数値計算法

    2017  

     View Summary

    本研究では反応拡散モデルに対する精度保証付き数値計算手法を開発した。特に正値解を対象とし、真の解を数学的に厳密な意味で数値的に包含する手法を提案した。即ち真の解が数値的に求めた近似解の付近に存在することを具体的な誤差上限と共に保証し、更に正負の怪しい領域における固有値問題を考えることによりその正値性をも数学的に厳密な意味で保証した。

 

Syllabus

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Social Activities

  • Introduction to Verified Numerical Computation

    JSTさくらサイエンスプラン 

    2021.02
     
     

  • 偏微分方程式に対する精度保証付き数値計算と符号変化構造解析への応用

    京都大学応用数学セミナー(KUAMS) 

    2019.12
     
     

  • 計算数理科学(複雑現象解明のための革新的な数値計算法,シミュレーション技術,アルゴリズムの開発)

    早稲田オープン・イノベーション・フォーラム 2019 

    2019.03
     
     

Academic Activities

  • 学会誌『応用数理』編集委員

    Other

    2019.04
    -
    Now

     View Summary

    2020年4月より主査

  • 第5回 JST 数学領域 未解決問題ワークショップ

    Academic society, research group, etc.

    国立研究開発法人 科学技術振興機構(JST)  

    2021.09
     
     
  • Organizer of Minisymposium "Numerical verification methods and their application to differential equations"

    Competition, symposium, etc.

    2019.07
     
     
  • Organization Committee, Secretary, The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN 2018)

    Competition, symposium, etc.

    2018.09
     
     
  • Local Organizer, SIAM Conference on Parallel Processing for Scientific Computing

    Competition, symposium, etc.

    2018.03