419 citations · 448 across the 27 of their papers we have counts for
5 papers · 1 filter
Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems
Kaname Matsue
We provide a rigorous numerical computation method to validate tubular neighborhoods of normally hyperbolic slow manifolds with the explicit radii for the fast-slow system \begin{e…
On blow-up solutions of differential equations with Poincaré-type compactifications
Kaname Matsue
We provide explicit criteria for blow-up solutions of autonomous ordinary differential equations. Ideas are based on the quasi-homogeneous desingularization (blowing-up) of singula…
Numerical validation of blow-up solutions of ordinary differential equations
Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki +3
This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on c…
On the construction of Lyapunov functions with computer assistance
Kaname Matsue, Tomohiro Hiwaki, Nobito Yamamoto
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for construc…
A note on the spectral mapping theorem of quantum walk models
Kaname Matsue, Osamu Ogurisu, Etsuo Segawa
We discuss the description of eigenspace of a quantum walk model with an associating linear operator in abstract settings of quantum walk including the Szegedy walk on grap…