Detailed Information

Research Field/Keywords for Research Field

• Numerical Analysis, Mathematical Programming, Optimization, Applied Mathematics

Education

• 2005/03, Hirosaki University, Department of Mathematical System Science, Graduated
• 2010/03, Hirosaki University, Graduate School of Science and Technology, Doctor Course, Completed

Employment Experience

• 2010/04 - 2012/03 Researcher Sasebo National College of Technology
• 2012/04 - 2015/03 Junior Researcher Waseda University
• 2015/04 -  *  Associate Professor, Information Science, Graduate School of Science and Engineering, Saga University
• 2015/04 - 9999/99 Adjunct Researcher Waseda University
• 2016/04 - 2018/03 Part-time Lecturer Sasebo National College of Technology

Field of Specialization

• Foundations of mathematics/Applied mathematics, Computational science, High performance computing, Mathematical informatics

Membership in Academic Societies

• JSIAM (The Japan Society for Industrial and Applied Mathematics), MSJ (The Mathematical Society of Japan)

Themes for Ongoing Research

• Numerical verification method by applying the matrix exponential
• Research on numerical verification for nonlinear minimization problems
• Numerical verification method of solutions for nonlinear evolutional equations

Research Themes in the Past

• Research on numerical verification for nonlinear minimization problems
• Numerical verification method of solutions for nonlinear evolutional equations

Original Articles

• Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation;　2022/05
  ANNOUNCEMENT INFO.;　Computational Methods in Applied Mathematics, Volume 22, Issue 3, 631-647
  AUTHOR;　Takuma Kimura, Teruya Minamoto and Mitsuhiro T. Nakao
  
• Constructive error estimates for full discrete approximation of periodic solution for heat equation;　2020/04
  ANNOUNCEMENT INFO.;　Journal of Computational and Applied Mathematics, Volume 368, Article 112510, 10 pp.
  AUTHOR;　Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
  
• Constructive error analysis of a full-discrete finite element method for the heat equation;　2019/04
  ANNOUNCEMENT INFO.;　Japan Journal of Industrial and Applied Mathematics, 36, 777–790
  AUTHOR;　Kouji Hashimoto, Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
  
• On the constructive error estimates of a full discrete approximation for time-periodic solution of the heat equations;　2018/09
  ANNOUNCEMENT INFO.;　The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations, 166--167
  AUTHOR;　Takuma Kimura, Teruya Minamoto and Mitsuhiro T. Nakao
  
• Optimal order constructive a priori error estimates for a full discrete approximation of the heat equation;　2017/09
  ANNOUNCEMENT INFO.;　Reliable Computing, 25, 202-212
  AUTHOR;　Takuma Kimura, Teruya Minamoto, and Mitsuhiro T. Nakao
  
• A method for verifying the accuracy of numerical solutions of symmetric saddle point linear systems;　2016/11
  ANNOUNCEMENT INFO.;　Numerical Algorithms, 76, 33-51
  AUTHOR;　Ryo Kobayashi, Takuma Kimura, Shin’ichi Oishi
  
• Optimal order constructive a priori error estimates for a full discrete approximation of the heat equation;　2016/09
  ANNOUNCEMENT INFO.;　17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 72-73
  AUTHOR;　Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
  
• A method of verified computation for convex programming;　2016/09
  ANNOUNCEMENT INFO.;　17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 121-122
  AUTHOR;　Ryo Kobayashi, Takuma Kimura, Shin’ichi Oishi
  
• Some considerations of the invertibility verifications for linear elliptic operators;　2015/03
  ANNOUNCEMENT INFO.;　Japan Journal of Industrial and Applied Mathematics, 32, 1, 19-31
  AUTHOR;　Nakao, M.T., Watanabe, Y., Kinoshita, T., Kimura, T., Yamamoto, N.
  
• On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems;　2014/04
  ANNOUNCEMENT INFO.;　Numerische Mathematik, 126, 4, 679-701
  AUTHOR;　Kinoshita Takehiko;Kimura Takuma;Nakao Mitsuhiro T.
  
• Validated Solutions for Symmetric Saddle Point Linear Systems;　2014
  ANNOUNCEMENT INFO.;　The 33rd JSST Annual Conference: International Conference on Simulation Technology, 90-91
  AUTHOR;　R. Kobayashi, T. Kimura, S. Oishi:
  
• Some remarks on the instability of approximate solutions for ODEs;　2013
  ANNOUNCEMENT INFO.;　Nonlinear Theory and Its Applications, 4, 1, 80-87
  AUTHOR;　Kimura Takuma;Kinoshita Takehiko;Nakao Mitsuhiro T.
  
• Validated solutions for P-matrix linear complementarity problems, ;　2013
  ANNOUNCEMENT INFO.;　Pacific Journal of Optimization, 9, 3, 479-491
  AUTHOR;　T. Kimura
  
• Constructive a priori error estimates for a full discrete approximation of the heat equation;　2013
  ANNOUNCEMENT INFO.;　SIAM Journal on Numerical Analysis, 51, 1525-1541
  AUTHOR;　M.T. Nakao, T. Kimura, T. Kinoshita
  
• On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems;　2012
  ANNOUNCEMENT INFO.;　Computing, 94, 151-162
  AUTHOR;　M.T. Nakao, T. Kinoshita, T. Kimura
  
• A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations;　2011
  ANNOUNCEMENT INFO.;　Journal of Computational and Applied Mathematics, 236, 1622-1636
  AUTHOR;　T. Kinoshita, T. Kimura, M.T. Nakao
  
• Validated solutions of saddle point linear systems;　2009
  ANNOUNCEMENT INFO.;　SIAM Journal on Matrix Analysis and Applications, 30, 1697-1708
  AUTHOR;　T. Kimura, X. Chen
  
• Kepler's octic curve as a model of Mars's orbit;　2009
  ANNOUNCEMENT INFO.;　Far East Journal of Applied Mathematics, 34, 21-30
  AUTHOR;　T. Kimura, H. Nakazato
  
• Topological properties of the numerical range of matrix polynomials;　2008
  ANNOUNCEMENT INFO.;　International Journal of Algebra, 2, 217-221
  AUTHOR;　T. Kimura, H. Nakazato
  
• Kepler's quartic curve as a model of planetary orbits;　2008
  ANNOUNCEMENT INFO.;　International Mathematical Forum, 3, 38, 1871-1877
  AUTHOR;　T. Kimura, H. Nakazato
  
• Verification of solutions for linear equations by RICCG method;　2007
  ANNOUNCEMENT INFO.;　International Journal of INFORMATION, 10, 741-751
  AUTHOR;　T. Kimura
  
• Finite element surface fitting for bridge management;　2006
  ANNOUNCEMENT INFO.;　International Journal of Information Technology & Decision Making, 5, 671-681
  AUTHOR;　X. Chen, T. Kimura
  

General Lectures

• [04568] Constructive error estimates for a full-discretized periodic solution of heat equation;　2023/08
  ANNOUNCEMENT INFO.;　10th International Congress on Industrial and Applied Mathematics (ICIAM 2023)
  AUTHOR;　Takuma Kimura (Saga University), Teruya Minamoto (Saga University), Mitsuhiro T. Nakao (Waseda University)