419 citations · 448 across the 27 of their papers we have counts for
6 papers · 1 filter
A Green's Function-Based Enclosure Framework for Poisson's Equation and Generalized Sub- and Super-Solutions
Kazuaki Tanaka, Ryoga Iwanami, Kaname Matsue +1
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conve…
Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity
Kaname Matsue, Akitoshi Takayasu
Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations. As an example, the finite di…
Rigorous numerics of finite-time singularities in dynamical systems - methodology and applications
Kaname Matsue
This paper aims at providing rigorous numerical computation procedure for finite-time singularities in dynamical systems. Combination of time-scale desingularization as well as Lya…
Numerical validation of blow-up solutions with quasi-homogeneous compactifications
Kaname Matsue, Akitoshi Takayasu
We provide a numerical validation method of blow-up solutions for finite dimensional vector fields admitting asymptotic quasi-homogeneity at infinity. Our methodology is based on q…
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…