Assistant Professor

Faculty of Engineering, Information and Systems

University of Tsukuba

Rigorous numerical computations for solutions of differential equations (ODEs and PDEs) are main interests of my study. A number of computer-assisted methods based on verified numerical computations for proving the existence and local uniqueness of solutions to various elliptic equations have been developed and improved over the last two decades by many researchers. My current interest is to validate the blow-up solutions of ODEs and to develop numerical methods of verified computing for parabolic and hyperbolic equations.

- Nov. 26-Dec. 1, Dagstuhl Seminar, Wadern, Germany.
- Aug. 21-23, 若手研究集会「波動・振動・流れの制御と逆問題 -理論と数値計算-」, Kyoto, Japan.
- Mar. 30, 応用数学セミナー, Saitama, Japan.
- Mar. 24-27, 日本数学会2017年度年会, Tokyo, Japan.
- Mar. 14-18, INVA 2017, Okinawa, Japan.
- Mar. 6-7, 日本応用数理学会2017年 研究部会連合発表会, Tokyo, Japan.
- Feb. 21-23, JST camp, Kagawa, Japan.
- Feb. 14-15, 非線形現象と高精度高品質数値解析, Toyama, Japan.

- A. Takayasu, M. Mizuguchi, T. Kubo, and S. Oishi:
*"Accurate method of verified computing for solutions of semilinear heat equations"*, submitted 2016. (arXiv:1611.10243)

Code associated to the paper is available here. - A. Takayasu, K. Matsue, T. Sasaki, K. Tanaka, M. Mizuguchi, and S. Oishi:
*"Numerical validation of blow-up solutions of ordinary differential equations"*, J. Comput. Appl. Math., Vol. 314, pp. 10-29, Apr. 2017 (available online Oct. 2016). (DOI:10.1016/j.cam.2016.10.013, arXiv:1606.03039) - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:
*"On the embedding constant of the Sobolev type inequality for fractional derivatives"*, NOLTA, IEICE, Vol. 7, No. 3, pp. 386-394, Jul. 2016. (DOI:10.1587/nolta.7.386, PDF) - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:
*"Numerical verification for existence of a global-in-time solution to semilinear parabolic equations"*, J. Comput. Appl. Math., Vol. 315, pp. 1-16, May. 2017 (available online Nov. 2016). (DOI:10.1016/j.cam.2016.10.024, PDF) - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:
*"A method of verified computations for solutions to semilinear parabolic equations using semigroup theory"*, to appear in SIAM J. Numer. Anal. (PDF) - N. Hoffman, K. Ichihara, M. Kashiwagi, H. Masai, S. Oishi, and A. Takayasu:
*"Verified computations for hyperbolic 3-manifolds"*, Exp. Math., Vol. 25, Issue 1, pp. 66-78, 2016. (available online Oct. 2015). (DOI:10.1080/10586458.2015.1029599, arXiv:1310.3410)

Code associated to the paper is available here. - K. Tanaka, A. Takayasu, X. Liu, S. Oishi:
*"Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation"*, Jpn. J. Ind. Appl. Math., Vol. 31, Issue 3, pp. 665-679, Nov. 2014. (DOI:10.1007/s13160-014-0156-2) - A. Takayasu, X. Liu, S. Oishi:
*"Remarks on computable a priori error estimates for finite element solutions of elliptic problems"*, NOLTA, IEICE, Vol. 5, No. 1, pp. 53-63, Jan. 2014. (DOI:10.1587/nolta.5.53) - K. Sekine, A. Takayasu, S. Oishi:
*"An algorithm of identifying parameters satisfying a sufficient condition of Plum's Newton-Kantorovich like existence theorem for nonlinear operator equations"*, NOLTA, IEICE, Vol. 5, No. 1, pp. 64-79, Jan. 2014. (DOI:10.1587/nolta.5.64) - A. Takayasu, X. Liu, S. Oishi:
*"Verified computations to semilinear elliptic boundary value problems on arbitrary polygonal domains"*, NOLTA, IEICE, Vol. 4, No. 1, pp. 34-61, Jan. 2013. (DOI:10.1587/nolta.4.34)

- Codes of "Accurate method of verified computing for solutions of semilinear heat equations" (requires Matlab and Intlab)
- HIKMOT - Verified computations for hyperbolic 3-manifolds -