11 citations · 20 across the 14 of their papers we have counts for
9 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…
Numerical verification method for positive solutions of elliptic problems
Kazuaki Tanaka
The purpose of this paper is to propose methods for verifying the positivity of a weak solution of an elliptic problem assuming -error estimation $ \left\|u-\hat{u}\…
A posteriori verification of the positivity of solutions to elliptic boundary value problems
Kazuaki Tanaka, Taisei Asai
The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither -regula…
Numerical verification for asymmetric solutions of the Hénon equation on bounded domains
Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi
The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore,…
Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi
In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We revea…
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…
Sharp numerical inclusion of the best constant for embedding on bounded convex domain
Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi +1
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on bounded conv…