Updated on 2024/03/29

写真a

 
MIZUGUCHI　Makoto
 
Organization
Faculty of Science and Engineering Research Associate
External link

Degree

  • 博士（工学） ( 早稲田大学 )

  • 修士（理学） ( 早稲田大学 )

Education

  • 2017.2
     

    Waseda University   doctor course   completed

  • 2013.3
     

    Waseda University   master course   completed

  • 2011.3
     

    Gakushuin University   graduated

Research History

  • 2021.4 - Now

    Chuo University   Assistant Professor

  • 2018.9 - 2021.3

    早稲田大学 理工学術院   基幹理工学部 応用数理学科   講師

  • 2018.4 - 2018.9

    早稲田大学 理工学術院   次席研究員(研究院講師)

  • 2017.4 - 2018.3

    早稲田大学 理工学術院   次席研究員(研究院助教)

Professional Memberships

  • 日本シミュレーション学会

  • 日本数学会

  • 日本応用数理学会

Research Interests

  • 偏微分方程式

  • 計算機援用証明

  • 精度保証付き数値計算

Research Areas

  • Natural Science / Applied mathematics and statistics

Papers

  • 抽象的なHilbert空間の有限次元部分空間への直交射影の誤差に対する最良定数 Reviewed

    高橋宗久, 関根晃太, 水口信

    日本応用数理学会論文誌   34 ( 1 )   19 - 32   2024.3

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

    DOI： 10.11540/jsiamt.34.1_19

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  • Rigorous numerical inclusion of the blow-up time for the Fujita-type equation Reviewed

    Makoto Mizuguchi, Kouta Sekine, Kouji Hashimoto, Mitsuhiro T. Nakao, Shin’ichi Oishi

    Japan Journal of Industrial and Applied Mathematics   40 ( 1 )   665 - 689   2022.11

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    Multiple studies have addressed the blow-up time of the Fujita-type equation. However, an explicit and sharp inclusion method that tackles this problem is still missing due to several challenging issues. In this paper, we propose a method for obtaining a computable and mathematically rigorous inclusion of the $$L^2(\varOmega )$$ blow-up time of a solution to the Fujita-type equation subject to initial and Dirichlet boundary conditions using a numerical verification method. More specifically, we develop a computer-assisted method, by using the numerically verified solution for nonlinear parabolic equations and its estimation of the energy functional, which proves that the concerned solution blows up in the $$L^2(\varOmega )$$ sense in finite time with a rigorous estimation of this time. To illustrate how our method actually works, we consider the Fujita-type equation with Dirichlet boundary conditions and the initial function $$u(0,x)=\frac{192}{5}x(x-1)(x^2-x-1)$$ in a one-dimensional domain $$\varOmega$$ and demonstrate its efficiency in predicting $$L^2(\varOmega )$$ blow-up time. The existing theory cannot prove that the solution of the equation blows up in $$L^2(\varOmega )$$. However, our proposed method shows that the solution is the $$L^2(\varOmega )$$ blow-up solution and the $$L^2(\varOmega )$$ blow-up time is in the interval (0.3068, 0.317713].

    DOI： 10.1007/s13160-022-00545-8

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    Other Link： https://link.springer.com/article/10.1007/s13160-022-00545-8/fulltext.html

  • Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation Reviewed

    Makoto Mizuguchi, Mitsuhiro T. Nakao, Kouta Sekine, Shin’ichi Oishi

    Journal of Scientific Computing   89 ( 2 )   2021.11

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    <title>Abstract</title>In this paper, we propose <inline-formula><alternatives><tex-math>$$L^2(J;H^1_0(\Omega ))$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
    <mml:mrow>
    <mml:msup>
    <mml:mi>L</mml:mi>
    <mml:mn>2</mml:mn>
    </mml:msup>
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    <mml:mo>(</mml:mo>
    <mml:mi>J</mml:mi>
    <mml:mo>;</mml:mo>
    <mml:msubsup>
    <mml:mi>H</mml:mi>
    <mml:mn>0</mml:mn>
    <mml:mn>1</mml:mn>
    </mml:msubsup>
    <mml:mrow>
    <mml:mo>(</mml:mo>
    <mml:mi>Ω</mml:mi>
    <mml:mo>)</mml:mo>
    </mml:mrow>
    <mml:mo>)</mml:mo>
    </mml:mrow>
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    </mml:math></alternatives></inline-formula> and <inline-formula><alternatives><tex-math>$$L^2(J;L^2(\Omega ))$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
    <mml:mrow>
    <mml:msup>
    <mml:mi>L</mml:mi>
    <mml:mn>2</mml:mn>
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    <mml:mo>;</mml:mo>
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    </mml:math></alternatives></inline-formula> norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible.

    DOI： 10.1007/s10915-021-01636-3

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    Other Link： https://link.springer.com/article/10.1007/s10915-021-01636-3/fulltext.html

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

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

    Journal of Inequalities and Applications   2017   2017.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    © 2017, The Author(s). This paper is concerned with an explicit value of the embedding constant from W1,q(Ω) to Lp(Ω) for a domain Ω ⊂ RN (N∈ N), where 1 ≤ q≤ p≤ ∞. 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 Ω 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 Ω to a domain dividable into bounded convex domains.

    DOI： 10.1186/s13660-017-1571-0

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    Other Link： http://link.springer.com/article/10.1186/s13660-017-1571-0/fulltext.html

  • Accurate method of verified computing for solutions of semilinear heat equations Reviewed

    Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'chi Oishi

    Reliable Computing   25   74 - 99   2017.7

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • Numerical verification for existence of a global-in-time solution to semilinear parabolic equations Reviewed

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    Journal of Computational and Applied Mathematics   315   1 - 16   2017.5

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.cam.2016.10.024

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

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

    Journal of Computational and Applied Mathematics   314   10 - 29   2017.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.cam.2016.10.013

    CiNii Books

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  • Sharp numerical inclusion of the best constant for embedding H_1^0(\Omega) \hookedrightarrow L^p (\Omega) on bounded convex domain Reviewed

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

    Journal of Computational and Applied Mathematics   311   306 - 313   2017.2

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.cam.2016.07.021

    Web of Science

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  • A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory Reviewed

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    SIAM Journal on Numerical Analysis   55 ( 2 )   980 - 1001   2017.1

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Society for Industrial & Applied Mathematics (SIAM)  

    DOI： 10.1137/141001664

    CiNii Books

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  • On the embedding constant of the Sobolev type inequality for fractional derivatives Reviewed

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    Nonlinear Theory and Its Applications, IEICE   7 ( 3 )   386 - 394   2016

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electronics, Information and Communications Engineers (IEICE)  

    This paper is concerned with the embedding constant of the Sobolev type inequality for fractional derivatives on $\Omega\subset\mathbb{R}^{N}~(N\in\mathbb{N})$. The constant is explicitly described using the analytic semigroup over L2(Ω) generated by the Laplace operator. Some numerical examples of estimating the embedding constant are also provided.

    DOI： 10.1587/nolta.7.386

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  • Verified computations for solutions to semilinear parabolic equations using the evolution operator Reviewed

    Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin’ichi Oishi

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   9582   218 - 223   2016

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

    This article presents a theorem for guaranteeing existence of a solution for an initial-boundary value problem of semilinear parabolic equations. The sufficient condition of our main theorem is derived by a fixed-point formulation using the evolution operator. We note that the sufficient condition can be checked by verified numerical computations.

    DOI： 10.1007/978-3-319-32859-1_18

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

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

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2015 ( 1 )   2015.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER INTERNATIONAL PUBLISHING AG  

    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： 10.1186/s13660-015-0907-x

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  • Numerical verification of positiveness for solutions to semilinear elliptic problems Reviewed

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

    JSIAM Letters   7   73 - 76   2015

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：The Japan Society for Industrial and Applied Mathematics  

    In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic boundary value problems. We provide a sufficient condition for a solution to an elliptic problem to be positive in the domain of the problem, which can be checked numerically without requiring a complicated computation. Although we focus on the homogeneous Dirichlet case in this paper (in fact, it is often possible that solutions are not positive near the boundary in this case), our method can be applied naturally to other boundary conditions. We present some numerical examples.

    DOI： 10.14495/jsiaml.7.73

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MISC

Presentations

  • 発展作用素を用いた初期値問題の精度保証付き数値計算～単調性を用いた爆発解検証への適用について～

    橋本 弘治, 水口 信, 関根 晃太, 中尾 充宏

    第20回 日本応用数理学会 研究部会連合発表会  2024.3 

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    Event date： 2024.3 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 発展作用素を用いた初期値問題の精度保証付き数値計算～変則的位相を用いた大域解検証への適用について～

    橋本 弘治, 水口 信, 関根 晃太, 中尾 充宏

    第20回 日本応用数理学会 研究部会連合発表会  2024.3 

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    Event date： 2024.3 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 放物型方程式の全離散近似解に対する定量的な誤差評価

    水 口 信, 中 尾 充 宏, 橋 本 弘 治, 関 根 晃 太, 大 石 進 一

    2023年度 日本数学会 秋季総合分科会  2023.9 

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    Event date： 2023.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • The best constants for the projection error on triplet Hilbert spaces

    Munehisa Takahashi, Kouta Sekine, Makoto Mizuguchi

    Japan Society for Simulation Technology (JSST2023)  2023.8 

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    Event date： 2023.8 　 　

    Language：English   Presentation type：Oral presentation (general)  

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  • 3つのHilbert空間の組における最良な射影誤差定数について

    高橋 宗久, 関根 晃太, 水口 信

    日本応用数理学会2022年度年会  2022.9 

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    Event date： 2022.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 放物型方程式の全離散近似に対する誤差評価について

    水口 信, 中尾 充宏, 橋本 弘治, 関根 晃太, 大石 進一

    日本応用数理学会2022年度年会  2022.9 

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    Event date： 2022.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Numerical verification method for a blow-up solution of Fujita-type equation

    Makoto Mizuguchi

    International Workshop on Reliable Computing and Computer-Assisted Proofs (ReCAP 2022)  2022.3 

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    Event date： 2022.3 　 　

    Language：English   Presentation type：Oral presentation (general)  

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  • 放物型方程式の半離散近似に対する誤差定数値の評価について

    水口 信

    第5回 精度保証付き数値計算の実問題への応用研究集会 (NVR 2021) ・ JST/CREST「モデリングのための精度保証付き数値計算論の展開」成果報告会  2021.11 

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    Event date： 2021.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 藤田型方程式の解の爆発時間に対する数値的検証法 Invited

    水口 信

    有限時間特異性の包括的記述に向けた 数学解析・計算機援用解析の展開「有限時間特異性」勉強会 第3回  2021.9 

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    Event date： 2021.9 　 　

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • 楕円型方程式と放物型方程式に対する半離散ガレルキン近似の誤差定数について

    水口 信, 中尾 充宏, 関根 晃太, 大石 進一

    日本応用数理学会2021年度年会  2021.9 

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    Event date： 2021.9 　 　

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  • 藤田型方程式の解の爆発時間に対する計算機を用いた数値的包含方法について

    水口信, 関根 晃太, 橋本 弘治, 中尾充宏, 大石 進一

    2020年度 応用数学合同研究集会  2020.12 

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  • 線形熱方程式の解と半離散近似解との誤差評価の改善

    水口 信, 中尾 充宏, 関根晃太, 大石 進一

    2019年日本応用数理学会年会  2019.9 

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  • 半線形熱方程式の解の精度保証付き数値計算法について Invited

    水口信, 関根 晃太, 中尾充宏, 大石進一

    第2回 精度保証付き数値計算の実問題への応用研究集会  2018.12 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • Estimation of Sobolev embedding constant on a bounded convex domain

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

    18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN'2018)  2018.9 

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    Language：English   Presentation type：Oral presentation (general)  

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  • A numerical verification method for solutions to systems of parabolic equations

    Makoto Mizuguchi, Kouta Sekine, Shin'ichi Oishi

    The International Workshop on Numerical Verification and its Applications (INVA2017)  2017.3 

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  • Lotka-Volterra型偏微分方程式の初期値境界値問題の解に対する精度保証付き数値計算法について

    水口信, 関根晃太, 大石進一

    2016年日本応用数理学会年会  2016.9 

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  • Verification algorithm for enclosing a mild solution of semilinear heat equations

    Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    The fifth Asian conference on Nonlinear Analysis and Optimization (NAO-Asia 2016)  2016.8 

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  • 重み付きラプラス作用素の分数べきに対する計算可能なソボレフの埋め込み定数

    水口信, 高安亮紀, 久保隆徹, 大石進一:

    日本数学会2016年度年会  2016.3 

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  • Verified computations for solutions of semilinear heat equations using an analytic semigroup generated by a self-adjoint operator

    Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    The 34th JSST Annual Conference International Conference on Simulation Technology (JSST2015)  2015.10 

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  • ある自己共役作用素から生成される解析半群を用いた半線形熱方程式の解の数値的検証法

    水口信, 関根晃太, 高安亮紀, 久保隆徹, 大石進一

    日本応用数理学会2015年度年会  2015.9 

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  • 発展方程式の解に対する精度保証付き数値計算法を用いた時間大域解の存在証明

    水口信, 高安亮紀, 久保隆徹, 大石進一

    精度保証付き数値計算の最近の展開,  2015.3 

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  • 半線形熱方程式の解に対する精度保証付き数値計算法を用いた時間大域解の存在証明

    水口信, 高安亮紀, 久保隆徹, 大石進一

    日本応用数理学会 2015年研究部会連合発表会  2015.3 

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  • Numerical verification of solutions for the Fujita type parabolic equations

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    The 14th Asia Simulation Conference & The 33rd JSST Annual Conference: International Conference on Simulation Technology (AsiaSim & JSST 2014)  2014.10 

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    Language：English   Presentation type：Oral presentation (general)  

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  • A sharper error estimate of verified computations for nonlinear heat equations

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN2014)  2014.9 

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  • A method of verified computations for nonlinear parabolic equations

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN2014)  2014.9 

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  • A method of verified computations for nonlinear homogeneous heat equations, Part II: Semigroup approach to construct an exact solution for time variable

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014)  2014.3 

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  • A method of verified computations for nonlinear homogeneous heat equations, Part I: Enclosure of semidiscrete approximate solution for space variable

    Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

    The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014)  2014.3 

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  • A priori error estimate of inhomogeneous heat equations using rational approximation of semigroups

    Makoto Mizuguchi, Takayuki Kubo, Akitoshi Takayasu, Shin'ichi Oishi

    International Conference on Simulation Technology (JSST 2013),  2013.9 

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  • 半群理論を用いた非斉次熱方程式の全離散近似解に対する事前誤差評価

    水口信, 久保隆徹, 高安亮紀, 大石進一

    日本応用数理学会 2013年研究部会連合発表会  2013.3 

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Awards

  • 第18回若手優秀講演賞

    2022.6   日本応用数理学会   楕円型方程式と放物型方程式に対する半離散ガレルキン近似の誤差定数について

    水口 信

  • Student Presentation Award

    2015.10   The 34th JSST Annual Conference International Conference on Simulation Technology (JSST2015)   Verified computations for solutions of semilinear heat equations using an analytic semigroup generated by a self-adjoint operator

    Makoto Mizuguchi

Research Projects

  • 半線形熱方程式の爆発解の厳密な爆発時間の解明と未知の実現象に対する研究基盤の確立

    Grant number：23K13018  2023.4 - 2028.3

    日本学術振興会  科学研究費助成事業  若手研究  中央大学

    水口 信

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    Grant amount： \4680000 （ Direct Cost: \3600000 、 Indirect Cost： \1080000 ）

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  • 精度保証付き数値計算法を用いた反応拡散系の大域解の解析

    Grant number：18K13462  2018.4 - 2023.3

    日本学術振興会  科学研究費助成事業  若手研究 

    水口 信

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    Grant amount： \4160000 （ Direct Cost: \3200000 、 Indirect Cost： \960000 ）

    放物型方程式の解の精度保障付き数値計算法において必要な半離散近似解に対する誤差評価の現状でベストな評価法を見つけ出して論文にまとめた.前述した通り楕円型方程式のリッツ誤差定数と一致するある意味で最良な評価を導き出した. そして当該年度においてその誤差定評価についての内容をまとめた論文が受理されることとなった.L^2(J;H^1)評価は2倍精度がよくなり, L^2(J;L^2)評価については4倍精度がよくなったことから放物型方程式の解の精度保障付き数値計算法による解の検証範囲が単純計算で2から8倍くらいまで拡張されたことになる.
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    昨年時に述べた研究である放物型方程式に対する爆発解の検証についても論文にまとめている最中である.本爆発解の研究は当該研究内容のある意味発展的な内容のひとつであり, 既存の放物型方程式の精度保証付き数値計算法とエネルギー汎関数による常微分方程式の爆発判定法を利用して爆発時間の上界と下界評価を得ることで爆発時刻を割り出す手法である.例えば,下界評価で0.5,上界評価で0.55とすれば, 爆発時間は区間[0.5,0.55]内にあると証明できる. よって厳密な爆発時間の範囲を割り出せることになる.昨年時では藤田型方程式限定の手法であったが,解の正の部分と負の部分を切り分けてその微分性をうまく利用することでより発展的な方程式に関しても同様な定式ができる可能性が浮上してきた.また, 初期値に対する符号変化にも対応できる可能性もあり本検証手法の拡張範囲の拡大も期待できる.

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Committee Memberships

  • 2020.4 - 2023.3

    学会誌「応用数理」   編集委員