Verified Computations for Solutions to Semilinear Parabolic Equations Using the Evolution Operator. - Akitoshi Takayasu; Makoto Mizuguchi; Takayuki Kubo; Shin'ichi Oishi (MACIS, 2015)

Verified Computations for Hyperbolic 3-Manifolds. - Neil Hoffman; Kazuhiro Ichihara; Masahide Kashiwagi; Hidetoshi Masai; Shin'ichi Oishi; Akitoshi Takayasu (Exp. Math., 2016)

Numerical verification for existence of a global-in-time solution to semilinear parabolic equations. - Makoto Mizuguchi; Akitoshi Takayasu; Takayuki Kubo; Shin'ichi Oishi (J. Comput. Appl. Math., 2017)

Numerical validation of blow-up solutions of ordinary differential equations. - Akitoshi Takayasu; Kaname Matsue; Takiko Sasaki; Kazuaki Tanaka; Makoto Mizuguchi; Shin'ichi Oishi (J. Comput. Appl. Math., 2017)

A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory. - Makoto Mizuguchi; Akitoshi Takayasu; Takayuki Kubo; Shin'ichi Oishi (SIAM J. Numer. Anal., 2017)

Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems. - Akira Imakura; Keiichi Morikuni; Akitoshi Takayasu (J. Comput. Appl. Math., 2020)

Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity. - Kaname Matsue; Akitoshi Takayasu (J. Comput. Appl. Math., 2020)

Numerical validation of blow-up solutions with quasi-homogeneous compactifications. - Kaname Matsue; Akitoshi Takayasu (Numerische Mathematik, 2020)

A geometric characterization of unstable blow-up solutions with computer-assisted proof. - Jean-Philippe Lessard; Kaname Matsue; Akitoshi Takayasu (CoRR, 2021)

Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity. - Jonathan Jaquette; Jean-Philippe Lessard; Akitoshi Takayasu (Commun. Nonlinear Sci. Numer. Simul., 2022)

Rigorous numerics for nonlinear heat equations in the complex plane of time. - Akitoshi Takayasu; Jean-Philippe Lessard; Jonathan Jaquette; Hisashi Okamoto (Numerische Mathematik, 2022)

Correction to: Rigorous numerics for nonlinear heat equations in the complex plane of time. - Akitoshi Takayasu; Jean-Philippe Lessard; Jonathan Jaquette; Hisashi Okamoto (Numerische Mathematik, 2022)

Complex moment-based methods for differential eigenvalue problems. - Akira Imakura; Keiichi Morikuni; Akitoshi Takayasu (Numer. Algorithms, 2023)

Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems. - Akira Imakura; Keiichi Morikuni; Akitoshi Takayasu (J. Comput. Appl. Math., 2023)

Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature. - Jean-Philippe Lessard; Kaname Matsue; Akitoshi Takayasu (J. Nonlinear Sci., 2023)

Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs. - Matthieu Cadiot; Jonathan Jaquette; Jean-Philippe Lessard; Akitoshi Takayasu (Commun. Nonlinear Sci. Numer. Simul., 2025)

Computer-assisted proofs for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces. - Toshimasa Ishige; Akitoshi Takayasu (CoRR, 2025)

A Rigorous Integrator and Global Existence for Higher-Dimensional Semilinear Parabolic PDEs via Semigroup Theory. - Gabriel William Duchesne; Jean-Philippe Lessard; Akitoshi Takayasu (J. Sci. Comput., 2025)