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
- Sep. 22-26, SCAN2025, Carl von Ossietzky Universität, Oldenburg, Germany.
- Jul. 7-18, Computer Assisted Proofs in Applied Mathematics (SLMath), Berkeley, CA, US.
- Jun. 22-28, DyToComp2025, Będlewo, Poland.
- May 11-15, SIAM DS25, Denver, Colorado, US.
- Mar. 18-21, 日本数学会 2025年度年会, 早稲田大学 早稲田キャンパス.
- Mar. 8, 日本応用数理学会 若手の会 第10回学生研究発表会, 岡山国際交流センター, 岡山.
- Mar. 5-7, 日本応用数理学会 第21回 研究部会連合発表会, 岡山大学 津島キャンパス.
- Feb. 20, 「有限時間特異性」勉強会 第11回, オンライン.
- Feb. 3-7, AIM SQuaREs, Caltech, CA, US.
Recent papers
- T. Ishige and A. Takayasu:
"Computer-assisted proofs for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces", submitted 2025. (arXiv:2501.03792 [math.NA])
- M. Cadiot, J. Jaquette, J.-P. Lessard, and A. Takayasu:
"Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs", submitted 2024. (arXiv:2411.18361 [math.NA])
- S. Kondo, A. Takayasu:
"Rigorous numerics via interval Chebyshev interpolation" (in Japanese), Transactions of the Japan Society for Industrial and Applied Mathematics, Vol. 34, No. 3, pp. 98-126, September 2024. (DOI:10.11540/jsiamt.34.3_98)
Code associated to the paper is available here.
- G. W. Duchesne, J.-P. Lessard, and A. Takayasu:
"A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory", J. Sci. Comput., Vol. 102, 62, 66 pages, January 2025. (DOI:10.1007/s10915-024-02785-x, arXiv:2402.00406 [math.AP])
- H. Kodani, K. Matsue, H. Ochiai, and A. Takayasu:
"Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence", Nonlinearity, Vol. 38, No. 4, 045004, 41 pages, March 2025. (DOI:10.1088/1361-6544/adb52e, arXiv:2211.06868 [math.CA])
- C.-M. Chen, T. Ishige, S. P. Kim, A. Takayasu, and C.-Y. Wei:
"Monodromy Approach to Pair Production of Charged Black Holes and Electric Fields", Chin. J. Phys., Vol. 86, pp. 255-268, December 2023. (DOI:10.1016/j.cjph.2023.10.007, arXiv:2210.14792 [hep-th])
- A. Imakura, K. Morikuni, and A. Takayasu:
"Complex moment-based methods for differential eigenvalue problems", Numer. Algor., Vol. 92, pp. 693-721, January 2023 (available online Dec. 2022).
(DOI:10.1007/s11075-022-01456-y, 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", J. Comput. Appl. Math., Vol. 424, 114994, 18 pages, May 2023 (available online Dec. 2022). (DOI:10.1016/j.cam.2022.114994, 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:
"Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature", J. Nonlinear Sci., Vol. 33, 46, 76 pages, March 2023 (available online March 2023). (DOI:10.1007/s00332-023-09900-6, 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", Numer. Math., Vol. 151, pp. 693-750, July 2022 (available online May 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.
- 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.
Google Scholar Citations
Codes
