11 citations · 42 across the 16 of their papers we have counts for
5 papers · 1 filter
Accurate method of verified computing for solutions of semilinear heat equations
Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo +1
We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqu…
Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine +1
This paper is concerned with an explicit value of the embedding constant from to for a bounded domain , where $1\leq…
Numerical verification method for positiveness of solutions to elliptic equations
Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi
In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an el…
Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents
Kazuaki Tanaka, Michael Plum, Kouta Sekine +2
The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane-Emden's equation with homogeneous Dirichlet boundary conditions. We pro…
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…