4 Result(s)

Article

Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature

In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining...

Jean-Philippe Lessard, Kaname Matsue, Akitoshi Takayasu in Journal of Nonlinear Science (2023)

Article

Complex moment-based methods for differential eigenvalue problems

This paper considers computing partial eigenpairs of differential eigenvalue problems (DEPs) such that eigenvalues are in a certain region on the complex plane. Recently, based on a “solve-then-discretize” par...

Akira Imakura, Keiichi Morikuni, Akitoshi Takayasu in Numerical Algorithms (2023)

Article

Correction to: Rigorous numerics for nonlinear heat equations in the complex plane of time

Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette… in Numerische Mathematik (2022)

Article

Rigorous numerics for nonlinear heat equations in the complex plane of time

In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explici...

Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette… in Numerische Mathematik (2022)