Research theme for competitive and other funds (6)：
2023 - 2026 Developments and Applications of Numerical Verification Methods for Finite Element Approximation of Differential Equations
2020 - 2024 Numerical Verification Methods for the Finite Element Approximation of Partial Differential Equations
2017 - 2021 Numerical verification method of solutions for evolutionary equations by applying the matrix exponential
2015 - 2018 A study on the numerical verification method of solutions with high accuracy for the nonlinear mathematical models in infinite dimension
2014 - 2017 Numerical Verification Method for Solutions of Nonlinear Programming Problems
2012 - 2015 Numerical verification method of solutions for nonlinear evolutional equations
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Papers (21)：
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao. Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method. Computers & Mathematics with Applications. 2025. 181. 248-258
Tomohiro Fukui, Takanori Hidane, Mikihide Demura, Takuma Kimura, Shintaro Morisada, Keisuke Ohto, Hidetaka Kawakita. Preparation of a Porous Spherical Adsorbent by Oil-In-Water-In-Oil Emulsion Polymerization for Phycocyanin Adsorption. Solvent Extraction and Ion Exchange. 2024
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao. Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation. Computational Methods in Applied Mathematics. 2022. 22. 3. 631-647
Takuma Kimura, Teruya Minamoto, Mitshuhiro T. Nakao. Constructive Error Estimates for a Full-Discretized Periodic Solution of Heat Equation by Spatial Finite-Element and Time Spectral Method. 10.2139/ssrn.4837039. 2024. 181. 248-258
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao. Constructive a priori error estimates for a full discrete approximation of periodic solutions for the heat equation. arXiv:1904.06067 [math.NA]. 2019
Kouji Hashimoto, Mitsuhiro T. Nakao, Takuma Kimura, Teruya Minamoto. Constructive error analysis of a full-discrete finite element method for the heat equation. arXiv:1806.07054 [math.NA]. 2018
木村 拓馬. A method of verified computation for convex programming. SCAN 2016 Book of Abstracts. 2016. -. 121-122
