11 citations · 42 across the 16 of their papers we have counts for
4 papers · 2 filters
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…
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…