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.

- Mar. 18-21, 日本数学会2018年度年会, Tokyo, Japan.
- Mar. 15-16, 日本応用数理学会 第14回 研究部会連合発表会, Osaka, Japan.
- Mar. 7-10, SIAM PP, Tokyo, Japan.
- Feb. 19, UTNAS, Tokyo, Japan.
- Feb. 13-14, 2018年軽井沢グラフと解析研究集会, Nagano, Japan.

- A. Takayasu, S. Yoon, and Y. Endo:
*"Rigorous numerical computations for 1D advection equations with variable coefficients"*, submitted 2018. (arXiv:1803.02960)

Code associated to the paper is available here. - K. Matsue and A. Takayasu:
*"Numerical validation of blow-up solutions with quasi-homogeneous compactifications"*, submitted 2017. (arXiv:1707.05936)

Code associated to the paper is available here. - A. Takayasu, M. Mizuguchi, T. Kubo, and S. Oishi:
*"Accurate method of verified computing for solutions of semilinear heat equations"*, Reliable computing, Vol. 25, pp. 74-99, July 2017. (PDF, 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"*, SIAM J. Numer. Anal., Vol. 55, No. 2, pp. 980-1001, Apr. 2017. (DOI:10.1137/141001664, 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 "Rigorous numerical computations for 1D advection equations with variable coefficients" (requires MATLAB with INTLAB and Chebfun)
- Codes of "Numerical validation of blow-up solutions with quasi-homogeneous compactifications" (requires c++ with boost libraries and kv libraries)
- Codes of "Accurate method of verified computing for solutions of semilinear heat equations" (requires MATLAB and INTLAB)
- HIKMOT - Verified computations for hyperbolic 3-manifolds -