Mitsuhiro NAKAO

Profile Information

Affiliation: Research Institute for Science and Engineering, Waseda University
: Professor, Faculty of Science and Engineering, Waseda University

Degree: (BLANK)(Kyushu University)

J-GLOBAL ID: 200901073323647211
researchmap Member ID: 1000043123

Research Interests

Research Areas

Research History

Apr, 2018 - Present

早稲田大学招聘研究員
Apr, 2010 - Present

Professor Emeritus (Professor Emeritus), Kyushu University
Dec, 2016 - Mar, 2018

Research Institute for Science and Engineering, Waseda University
Apr, 2010 - Mar, 2016

National Institute of Technology, Sasebo College
Apr, 2007 - Mar, 2010

九州大学産業技術数理研究センター長
May, 2009

Kyushu University
Aug, 2003 - Mar, 2008

21世紀COEプログラム「機能数理学の構築と展開」拠点リーダー
Jul, 2002 - Jul, 2006

Faculty of Mathematics, Kyushu University
Jun, 1994

九州大学教授（大学院数理学研究科, 2000年4 月より数理学研究院）
Oct, 1988

Kyushu University
Apr, 1982

九州工業大学講師（工学部）, 1984 年10 月同助教授
Jan, 1980

Kyushu University
Apr, 1974

日本電信電話公社（現NTT）横須賀電気通信研究所研究員

Education

Apr, 1984

理学博士（九州大学）
Mar, 1974

数学専攻修士課程修了, 理学研究科, 九州大学大学院
Mar, 1972

School of Sciences, Kyushu University
Mar, 1968

国立佐世保工業高等専門学校機械工学科卒業

Committee Memberships

2011 - Present

日本応用数理学会フェロー
2014 - Mar, 2022

科学技術振興機構 CREST 「現代の数理科学と連携するモデリング手法の構築」領域アドバイザー
2006 - 2017

日本学術会議連携会員
2008 - 2013

井上科学振興財団選考委員会委員
2008 - 2012

-: 日本数学会教育研究資金問題検討委員会委員
2012

大学評価・学位授与機構外部検証委員会委員
2007 - 2011

-: 京都大学数理解析研究所運営委員
1999 - 2002

-: 文部科学省理学視学委員

Awards

Apr, 2014

Prizes for Science and Technology, Research Category, Ministry of Education, Culture, Sports, Science and Technology

NAKAO Mitsuhiro T
Apr, 2014

文部科学大臣表彰科学技術賞（研究部門）

中尾充宏
Sep, 2012

Autumn Prize, The Mathematical Society of Japan

NAKAO Mitsuhiro T
Sep, 2012

日本数学会賞秋季賞
Sep, 2011

日本応用数理学会論文賞（JJIAM部門)
Dec, 2007

「ナイスステップな研究者」選定（文部科学省科学技術政策研究所）

Papers

Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

Computers & Mathematics with Applications, 181 248-258, Mar, 2025
Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

Computers and Mathematics with Applications, 181 248-258, Mar 1, 2025
Inclusion method of optimal constant with quadratic convergence for $H_0^1$-projection error estimates and its applications

Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao

Journal of Computational and Applied Mathematics, 417 114521-114521, Jan, 2023 Peer-reviewed
Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

JOURNAL OF SCIENTIFIC COMPUTING, 94(2), Jan, 2023
Rigorous numerical inclusion of the blow-up time for the Fujita-type equation

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

Japan Journal of Industrial and Applied Mathematics, 40(1) 665-689, Nov 5, 2022 Peer-reviewed
On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

Acta Cybernetica, 26(1) 71-82, Sep 2, 2022
Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains

Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi

Communications in Nonlinear Science and Numerical Simulation, 108, May, 2022
Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

Computational Methods in Applied Mathematics, May, 2022
A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems

Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi, Masahide Kashiwagi

Applied Numerical Mathematics, 169 87-107, Nov, 2021 Peer-reviewed
Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation

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

Journal of Scientific Computing, 89(2), Nov, 2021 Peer-reviewed
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

Xuefeng Liu, Mitsuhiro T. Nakao, Chun’guang You, Shin’ichi Oishi

Japan Journal of Industrial and Applied Mathematics, 38(2) 545-559, Jun, 2021
Numerical verification methods for a system of elliptic PDEs, and their software library

Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi

IEICE NONLINEAR THEORY AND ITS APPLICATIONS, 12(1) 41-74, 2021 Peer-reviewed
A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator

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

Numerische Mathematik, 146(4) 907-926, Oct, 2020 Peer-reviewed
Numerical Verification of Solutions for Nonlinear Parabolic Problems

Kouji Hashimoto, Takehiko Kinoshita, Mitsuhiro T. Nakao

Numerical Functional Analysis and Optimization, 41(12) 1495-1514, Sep 9, 2020
Some improvements of invertibility verifications for second-order linear elliptic operators

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Applied Numerical Mathematics, 154 36-46, Aug, 2020
Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

Journal of Computational and Applied Mathematics, 369 112561-112561, May, 2020
Constructive error estimates for full discrete approximation of periodic solution for heat equation

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

Journal of Computational and Applied Mathematics, 368, Apr 1, 2020 Peer-reviewed
Constructive error analysis of a full-discrete finite element method for the heat equation

Hashimoto Kouji, Kimura Takuma, Minamoto Teruya, Nakao Mitsuhiro T

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 36(3) 777-790, Sep, 2019 Peer-reviewed
An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Japan Journal of Industrial and Applied Mathematics, 36(2) 407-420, Jul, 2019 Peer-reviewed
An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

Journal of Differential Equations, 266(9) 5431-5447, Apr, 2019 Peer-reviewed

Misc.

有限要素法の構成的誤差評価とその計算機援用証明への応用 (現象解明に向けた数値解析学の新展開(2))

中尾充宏

数理解析研究所講究録, (2037) 54-56, Jul, 2017
放物型方程式の全離散近似解に対するオーダー最良な構成的誤差評価について

木村拓馬, 皆本晃弥, 中尾充宏

日本応用数理学会年会講演予稿集(CD-ROM), 2015 ROMBUNNO.9GATSU9NICHI,09:30,G,, Sep 2, 2015
Numerical verification method of solutions for nonlinear elliptic and evolutional problems (Mathematical Analysis of Viscous Incompressible Fluid)

Nakao Mitsuhiro T.

RIMS Kokyuroku, 1905 112-131, Jul, 2014
［short invited paper］放物型問題の解の検証における計算上の注意

木村拓馬, 木下武彦, 中尾充宏

ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集, 2013(2013) 122-122, Jan 8, 2013
偏微分方程式の解に対する精度保証付き数値計算

数学, 65 113-132, 2013 Peer-reviewedInvited
Reliability in numerical simulation(Review,<Special Feature>Reliability in numerical simulation)

Nakao Mitsuhiro

Journal of the Japan Society for Simulation Technology, 31(3) 133-135, Sep 15, 2012
放物型初期境界値問題の数値解に対する精度保証について (科学技術計算における理論と応用の新展開)

中尾充宏, 木村拓馬, 木下武彦

数理解析研究所講究録, 1791(1791) 112-121, Apr, 2012
常微分方程式の初期値問題に対する数値解の意外な挙動について (科学技術計算における理論と応用の新展開)

木村拓馬, 中尾充宏

数理解析研究所講究録, 1791(1791) 196-205, Apr, 2012
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems

Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura

COMPUTING, 94(2-4) 151-162, Mar, 2012
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems

Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura

Computing, 94(2-4) 151-162, Mar, 2012
線形化逆作用素を用いた非線形常微分方程式系に対する解の検証方法について

木下武彦, 木村拓馬, 中尾充宏

日本応用数理学会年会講演予稿集(CD-ROM), 2012 259-260, 2012
放物型初期値境界値問題に対する計算機援用証明について

木村拓馬, 木下武彦, 中尾充宏

日本応用数理学会年会講演予稿集(CD-ROM), 2012 291-292, 2012
A numerical verification method for a periodic solution of a delay differential equation

Teruya Minamoto, Mitsuhiro T. Nakao

Journal of Computational and Applied Mathematics, 235(3) 870-878, Dec 1, 2010
Delayed Feedback制御に基づくレスラー方程式の周期軌道に対する数値的検証法について (数値解析と数値計算アルゴリズムの最近の展開)

皆本晃弥, 中尾充宏

数理解析研究所講究録, 1719 97-105, Nov, 2010
Some eigenvalue excluding methods for infinite dimensional operators

Watanabe Yoshitaka, Nagatou Kaori, Plum Michael, Nakao Mitsuhiro T

RIMS Kokyuroku, 1719 118-129, Nov, 2010
Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems (vol 43, pg 388, 2010)

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoungnyoun Kim

JOURNAL OF SCIENTIFIC COMPUTING, 44(1) 107-107, Jul, 2010
Special Issue on State of the Art in Self-Validating Numerical Computations Preface

Mitsuhiro T. Nakao, Shin'ichi Oishi

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 26(2-3) 123-124, Oct, 2009
偏微分方程式の解に対する数値的存在検証-研究の原点とその展開-

中尾充宏

Fundamentals Review, 2(3) 19-28, 2009
A numerical verification method for solutions of nonlinear parabolic problems

Nakao Mitsuhiro T., Hashimoto Kouji

JMI, 1 69-72, 2009
A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 89(1) 5-18, Jan, 2009

Books and Other Publications

Numerical verification methods and computer-assisted proofs for partial differential equations

中尾, 充宏, Plum, Michael, 渡部, 善隆 (Role: Joint author)

Springer, Nov, 2019 (ISBN: 9789811376689)
実例で学ぶ精度保証付き数値計算---理論と実装---

サイエンス社, Oct, 2011
State of the Art for Self-Validating Numerical Computations, Special Issue of Japan Journal of Industrial and Applied Mathematics 26-2/3.

Kinokuniya, Tokyo, 2009
偏微分方程式から数値シミュレーションへ／計算の信頼性評価, 現代技術への数学入門シリーズ

講談社, 2008
Special Issue: Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004)

Journal of Computational and Applied Mathematics 199/2, Elsevier,, 2007
Numerical verification methods for solutions of free boundary problems

Proceedings of MSCOM Yamaguchi, 2000, LNCSE, Springer-Verlag, 2001
A guaranteed bound of the optimal constant in the error estimates for linear triangular element Part

Proceedings Volume for Invited Lectures of SCAN 2000, Springer-Verlag, 2001
精度保証付き数値計算

日本評論社, 1998
Guaranteed error bounds for finite element solutions of the Stokes problem

Scinetific computing and validated numerics, 1996
Computable L∞ error estimates in the finite element method with application to nonlinear elliptic problems

World Scientific Series in Appliable Analysis, 1993
Computable error estimates for FEM and numerical verifications of solutions for nonlinear PDEs

Computational and Applied Mathematics I (North-Holland), 1992

Professional Memberships

Research Projects

Computer-assisted solution verification for 3D flows with large Reynolds numbers

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2021 - Mar, 2025
Computer-assisted solution verification for 3D flows with large Reynolds numbers

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2021 - Mar, 2025
偏微分方程式の解に対する数値的検証法の新たな高度化の研究

科学研究費助成事業, 基盤研究(C), 日本学術振興会, Apr, 2021 - Mar, 2024

中尾充宏
Innovative research for self-validating numerical method of infinite dimensional problems

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2018 - Mar, 2022

NAKAO MITSUHIRO
A study on the numerical verification method of solutions with high accuracy for the nonlinear mathematical models in infinite dimension

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2015 - Mar, 2018

NAKAO Mitsuhiro, WATANABE Yoshitaka, KIMURA Takuma, KINOSHITA Takehiko, Michael Plum
Numerical verification method of solutions for nonlinear evolutional equations

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2015

NAKAO Mitsuhiro, KIMURA Takuma, WATANABE Yoshitaka, KINOSHITA Takehiko, MICHAEL Plum
Optimal estimation for inverse of infinite-dimensional operator by self-validating numerical computations and its applications

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2015

Yoshitaka Watanabe, Nagatou Kaori, Nakao Mitsuhiro T.
Development of computer assisted analysis for complicated nonlinear phenomena

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (S), Japan Society for the Promotion of Science, 2008 - 2011

NAKAO Mitsuhiro, EI Shin-ichiro, TABATA Masahisa, NAGATOU Kaori, MURASHIGE Sunao, YAMAMOTO Nobito, WATANABE Yoshitaka, OISHI Shinichi
Foundation of high accuracy computational methods on the multiple-precision computer environment and its applications to analysi of inverse problems

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2007 - 2009

ISO Yuusuke, NISHIMURA Naoshi, YAMAMOTO Yutaka, SUGIMOTO Naozou, FUJIWARA Hiroshi, HIGASHIMORI Nobuyuki, IMAI Hitoshi, NISHIDA Takaaki, OONISHI Kazuei, YAMAMOTO Masahiro, NISHIDA Kotoba, MATSUDA Tetsuya, OKAMOTO Hisashi, SAKAJYO Takashi, NAKAMURA Gen, TANUMA Kazumi, SHIROTA Kenji, NAKAO Mitsuhiro, TOMOEDA Kenji
Development and analysis of high-quality numerical methods and simulation for flow problems

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (S), Japan Society for the Promotion of Science, 2004 - 2008

TABATA Masahisa, NAKAO Mitsuhiro, NAKAKI Tatsuyuki, WATANABE Yoshitaka, KIMURA Masato, NAGATOU Kaori, SUZUKI Atushi
Research of applied analysis toward the global theory for nonlinear systems

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2005 - 2007

NISHIDA Takaaki, NAKAO Mitsuhiro, KOKUBU Hiroshi, KAWANAGO Tadashi, TANAKA kazunaga
数値処理と数式処理の融合による計算機援用解析学の可能性に関する基礎的研究

科学研究費助成事業, 萌芽研究, 日本学術振興会, 2005 - 2007

中尾充宏, 吉川敦, 横山和弘
Synthetic approach for the development of computer assisted analysis from the numerical verification methods

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science, 2003 - 2006

NAKAO Mitsuhiro, TABATA Masahisa, IMAI Hitoshi, TSUCHIYA Takuya, NISHIDA Takaaki, CHIN Shokun
Applied Analysis for Nonlinear Systems

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2002 - 2004

NISHIDA Takaaki, KOKUBU Hiroshi, KAWANA Tadashi, NAKAO Mitsuhiro T., KOZONO Hideo, MATSUMURA Akitaka
記号・代数計算による最適化問題解法と定理自動証明の研究

科学研究費助成事業, 萌芽研究, 日本学術振興会, 2002 - 2003

横山和弘, 吉川敦, 鈴木昌和, 中尾充弘, 穴井宏和
計算機による解析学創設の可能性に関する基礎的研究

科学研究費助成事業, 萌芽研究, 日本学術振興会, 2001 - 2003

中尾充宏, 渡部善隆, 吉川敦
Construction of Numerical Analysis for High-performance Large-Scale Computation

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science, 2001 - 2003

TABATA Masahisa, KANAYAMA Hiroshi, USHIJIMA Teruo, IMAI Hitoshi, NAKAO Mitsuhiro, KIKUCHI Fumio
Synthetic approach for new developments of self-validating numerics

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2001 - 2002

NAKAO Mitsuhiro, OISHI Shin'ichi, IMAI Hitoshi, ISO Yusuke, YAMAMOTO Tetsurou, NISHIDA Takaaki
Construction of a Practical Computation Code for Heat Convection Problems with Slow Flow

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 1999 - 2001

TABATA Masahisa, FUKUMOTO Yasuhide, HONDA Satoru, NAKAO Mitsuhiro, SUZUKI Atsushi, YAMAMOTO Nobito
Study on non-standard finite element approximation methods for partial differential equations

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 1999 - 2001

KAKO Takashi, TABATA Masahisa, KAWARADA Hideo, OHTSUKA Koji, ZHANG Shao-liang, NAKAO Mitushiro

Profile Information

Research Interests

Research Areas

Research History

Education

Committee Memberships

Awards

Papers

Misc.

Books and Other Publications

Professional Memberships

Research Projects

Menu

Coauthors