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
- Aug. 30-Sep. 2, SIAM NWCS22, University of Bremen, Bremen, Germany.
- Jul. 11-15, EQUADIFF 15, Masaryk University, Brno, Czech Republic.
- Jun. 19-25, DyToComp2022, Bedlewo, Poland.
- Mar. 13-18, ReCAP 2022, hybrid.
- Mar. 10, 日本応用数理学会 若手の会 第7回学生研究発表会, online.
- Mar. 8-9, 日本応用数理学会 第18回 研究部会連合発表会, online.
Recent papers
- A. Imakura, K. Morikuni, and A. Takayasu:
"Complex moment-based methods for differential eigenvalue problems", submitted 2022. (arXiv:2205.00971)
- 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", Commun. Nonlinear Sci. Numer. Simul., Vol. 107, 106188, 14 pages, April 2022 (available online Dec. 2021). (DOI:10.1016/j.cnsns.2021.106188, 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", Advances in Mathematics, Vol. 398, 108234, 70 pages, March 2022 (available online Feb. 2022). (DOI:10.1016/j.aim.2022.108234, 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", to appear in Numerische Mathematik, 2022. (DOI:10.1007/s00211-022-01291-2, 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:
"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)
Google Scholar Citations
Codes
