論文 / Publications

Preprint

1. Sora Sawai, Kazuaki Tanaka, Katsuhisa Ozaki, Shin'ichi Oishi: Polygonal Sequence-driven Triangulation Validator: An Incremental Approach to 2D Triangulation Verification, submitted. arXiv

Papers (Refereed)

1. Kazuaki Tanaka, Michael Plum, Kouta Sekine, Masahide Kashiwagi, and Shin'ichi Oishi: Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents, Numerical Functional Analysis and Optimization, 43 (3), 322-349 (2022). Journal arXiv

2. Kazuaki Tanaka, Taisei Asai: A posteriori verification of the positivity of solutions to elliptic boundary value problems, Partial Differential Equations and Application, 3, 9 (2022). Journal (Open Access)

3. Kouta Sekine, Kazuaki Tanaka, and Shin'ichi Oishi: Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems, Computers & Mathematics with Applications, 106, 18-26 (2022). Journal (Open Access)

4. Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi: Numerical verification for asymmetric solutions of the Hénon equation on bounded domains, Journal of Computational and Applied Mathematics, 399, 113708 (2022). Journal (Open Access)

5. Kazuaki Tanaka: A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations, Japan Journal of Industrial and Applied Mathematics, 38, 731-756 (2021). Journal (Open Access)

6. Yuta Matsushima, Kazuaki Tanaka, and Shin'ichi Oishi: Numerical verification for positive solutions of Allen–Cahn equation using sub- and super-solution method, Journal of Advanced Simulation in Science and Engineering, 7 (1), 136-150 (2020). Journal (Open Access)

7. Kazuaki Tanaka: Numerical verification method for positive solutions of elliptic problems, Journal of Computational and Applied Mathematics, 370, 112647 (2020). Journal arXiv

8. 酒井将大, 田中一成, 大石進一: 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, 日本応用数理学会論文誌, 29巻, 1号, 17-45 (2019). Journal (Open Access)

9. Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi: Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains, Journal of Inequalities and Applications, 299 (2017). Journal (Open Access)

10. Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, and Shin'ichi Oishi: Numerical validation of blow-up solutions of ordinary differential equations, Journal of Computational and Applied Mathematics, 314, 10–29 (2017). Journal arXiv

11. Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, and Shin'ichi Oishi: Sharp numerical inclusion of the best constant for embedding  on bounded convex domain, Journal of Computational and Applied Mathematics, 311, 306–313 (2017). Journal arXiv

12. Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, and Shin'ichi Oishi: Estimation of the Sobolev embedding constant on domains with minimally smooth boundary using extension operator, Journal of Inequalities and Applications, 389 (2015). Journal (Open Access)

13. Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, and Shin'ichi Oishi: Numerical verification of positiveness for solutions to semilinear elliptic problems, JSIAM Letters 7, 73-76 (2015). Journal (Open Access)

14. Kazuaki Tanaka, Akitoshi Takayasu, Xuefeng Liu, and Shin'ichi Oishi: Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation, Japan Journal of Industrial and Applied Mathematics, 31, 665-679 (2014). Journal

Papers (Non-refereed)

1. 関根晃太, 田中一成, 大石進一: 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, 京都大学数理解析研究所講究録 No.2037，現象解明に向けた数値解析学の新展開 II, 96-104, 2017. Journal (Open Access)

2. Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi: Numerical verification method for positivity of solutions to elliptic equations, RIMS Kôkyûroku No.2037, Numerical Analysis: New Developments for Elucidating Interdisciplinary Problems II, 125-140, 2017. Journal (Open Access)

Proceedings

1. Kouta Sekine, Kazuaki Tanaka, and Shin'ichi Oishi: Computer assisted existence proof of solutions to system of partial differential equations with bounded convex polygonal domains (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), Proceedings of the Twenty-Eighth RAMP Symposium, Niigata University, Niigata, October 13–14, 2016.

その他（解説記事など）

1. 田中一成, コンピュータも計算を間違う？－数値計算の精度と誤差－, 日本音響学会誌, 78巻10号, 2022.