Research Interests
Numerical analysis, rigorous numerics, computer-assisted proofs, partial differential equations, delay differential equations, ordinary differential equations, differential equations in the complex domain, blow-up solution of differential equations, infinite dimensional dynamical systems, fixed point methods, spectral methods, finite element method, semigroup theory.
(Travel) Schedule
2022
2021
- Dec. 17-19, 2021年度応用数学合同研究集会, online.
- Nov. 28, NVR 2021, online.
- Nov. 17-19, RIMS 時間遅れ系と数理科学：理論と応用の新たな展開に向けて, online.
- Sep. 13-17, SCAN2020,
Szeged, Hungary online.
- Sep. 7-9, 日本応用数理学会 2021年度 年会, online.
- Sep. 6, 日本応用数理学会 若手の会 若手研究交流会, online.
Jun. 17-21, AIMS, Atlanta, USA.- May 23-27, DS21, Virtual Conference.
- May. 14, 京都大学 NLPDE セミナー, online.
- Apr. 27, 数値解析セミナー(UTNAS), online.
- Mar. 15-18, 日本数学会2021年度年会, online.
- Mar. 8, 日本応用数理学会 若手の会 第6回学生研究発表会, online.
- Mar. 4-5, 日本応用数理学会 第17回 研究部会連合発表会, online.
- Jan. 25, 第2回時間遅れと数理セミナー, online.
- Jan. 5-7, Czech-Japanese Seminar in Applied Mathematics, online.
Recent papers
- A. Imakura, K. Morikuni, and A. Takayasu:
"Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems", submitted 2021. (arXiv:2110.01822)
- J. Jaquette, J.-P. Lessard, and A. Takayasu:
"Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity", submitted 2021. (arXiv:2109.00159)
Code associated to the paper is available here
- J.-P. Lessard, K. Matsue, and A. Takayasu:
"A geometric characterization of unstable blow-up solutions with computer-assisted proof", submitted 2021. (arXiv:2103.12390)
Code associated to the paper is available here.
- J. Jaquette, J.-P. Lessard, and A. Takayasu:
"Global dynamics in nonconservative nonlinear Schrödinger equations", submitted 2020. (arXiv:2012.09734)
Code associated to the paper is available here.
- A. Takayasu, J.-P. Lessard, J. Jaquette, and H. Okamoto:
"Rigorous numerics for nonlinear heat equations in the complex plane of time", submitted 2019. (arXiv:1910.12472)
Code associated to the paper is available here.
- A. Imakura, K. Morikuni, and A. Takayasu:
"Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems", J. Comput. Appl. Math., Vol. 369, 112543, 11 pages, May 2020 (available online Oct. 2019). (DOI:10.1016/j.cam.2019.112543, arXiv:1904.06277)
- K. Matsue and A. Takayasu:
"Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity", J. Comput. Appl. Math., Vol. 374, 112607, 11 pages, August 2020 (available online Jan. 2020). (DOI:10.1016/j.cam.2019.112607, arXiv:1902.01842)
Code associated to the paper is available here.
- A. Takayasu, S. Yoon, and Y. Endo:
"Rigorous numerical computations for 1D advection equations with variable coefficients", Japan J. Indust. Appl. Math., Vol. 36, No. 2, pp. 357-384, July 2019 (available online Feb. 2019). (DOI:10.1007/s13160-019-00345-7, 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", Numer. Math., Vol. 145, pp. 605-654, July 2020 (available online Jun. 2020). (DOI:10.1007/s00211-020-01125-z, 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.
Google Scholar Citations
Codes
