Mitsuhiro T. Nakao

42 papers Journal 37Unranked 4
YearRankTypeTitle / Venue / Authors
2025 J jnl
Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method.
Comput. Math. Appl.
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
2023 J jnl
Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces.
J. Sci. Comput.
Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
2023 J jnl
Inclusion method of optimal constant with quadratic convergence for H01-projection error estimates and its applications.
J. Comput. Appl. Math.
Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
2022 J jnl
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains.
Commun. Nonlinear Sci. Numer. Simul.
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
2022 J jnl
Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation.
Comput. Methods Appl. Math.
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
2022 J jnl
On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators.
Acta Cybern.
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
2021 J jnl
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains.
CoRR
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
2021 J jnl
Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation.
J. Sci. Comput.
Makoto Mizuguchi, Mitsuhiro T. Nakao, Kouta Sekine, Shin'ichi Oishi
2021 J jnl
Foreword.
J. Comput. Appl. Math.
Mitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump
2020 J jnl
A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator.
Numerische Mathematik
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
2020 J jnl
Constructive error estimates for full discrete approximation of periodic solution for heat equation.
J. Comput. Appl. Math.
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
2020 J jnl
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations.
CoRR
Xuefeng Liu, Mitsuhiro T. Nakao, Chun'guang You, Shin'ichi Oishi
2020 J jnl
Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space.
J. Comput. Appl. Math.
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
2019 J jnl
A new formulation for the numerical proof of the existence of solutions to elliptic problems.
CoRR
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
2017 J jnl
On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations.
JSIAM Lett.
Yoshitaka Watanabe, Mitsuhiro T. Nakao, Kaori Nagatou
2016 J jnl
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration.
Appl. Math. Comput.
Yoshitaka Watanabe, Mitsuhiro T. Nakao
2015 — conf
H
MACIS
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
2014 J jnl
On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems.
Numerische Mathematik
Takehiko Kinoshita, Takuma Kimura, Mitsuhiro T. Nakao
2014 — conf
Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators.
SCAN
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
2014 J jnl
Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces.
SIAM J. Numer. Anal.
Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao
2013 J jnl
A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations.
Math. Comput.
Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
2013 J jnl
Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation.
SIAM J. Numer. Anal.
Mitsuhiro T. Nakao, Takuma Kimura, Takehiko Kinoshita
2013 — conf
Some Remarks on the Optimal Error Estimates for the Finite Element Method on the L-Shaped Domain.
ITNG
Takehiko Kinoshita, Mitsuhiro T. Nakao
2012 J jnl
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems.
Computing
Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura
2011 J jnl
A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations.
J. Comput. Appl. Math.
Takehiko Kinoshita, Takuma Kimura, Mitsuhiro T. Nakao
2010 J jnl
A numerical verification method for a periodic solution of a delay differential equation.
J. Comput. Appl. Math.
Teruya Minamoto, Mitsuhiro T. Nakao
2010 J jnl
Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems.
J. Sci. Comput.
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoung-Nyoung Kim
2010 J jnl
Erratum to: Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems.
J. Sci. Comput.
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoungnyoun Kim
2010 J jnl
On very accurate enclosure of the optimal constant in the a priori error estimates for H
J. Comput. Appl. Math.
Takehiko Kinoshita, Mitsuhiro T. Nakao
2009 J jnl
A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems.
Numerische Mathematik
Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takaaki Nishida
2009 J jnl
On very accurate verification of solutions for boundary value problems by using spectral methods.
JSIAM Lett.
Mitsuhiro T. Nakao, Takehiko Kinoshita
2008 J jnl
Some remarks on the behaviour of the finite element solution in nonsmooth domains.
Appl. Math. Lett.
Mitsuhiro T. Nakao, Takehiko Kinoshita
2005 J jnl
A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems.
Computing
Mitsuhiro T. Nakao, Kouji Hashimoto, Yoshitaka Watanabe
2005 J jnl
SCAN'2004 11th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
Reliab. Comput.
Mitsuhiro T. Nakao, Kaori Nagatou
2004 J jnl
An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations.
Numer. Algorithms
Mitsuhiro T. Nakao, Yoshitaka Watanabe
2003 J jnl
Some Computer Assisted Proofs for Solutions of the Heat Convection Problems.
Reliab. Comput.
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida
2001 — ch.
A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Elements.
Perspectives on Enclosure Methods
Mitsuhiro T. Nakao, Nobito Yamamoto
1999 J jnl
A Numerical Verification Method of Solutions for the Navier-Stokes Equations.
Reliab. Comput.
Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
1998 — conf
A Numerical Verification Method of Solutions for the Navier-Stokes Equations.
SCAN
Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
1998 J jnl
Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations.
Reliab. Comput.
Mitsuhiro T. Nakao, Nobito Yamamoto, Yoshitaka Watanabe
1998 J jnl
Numerical verification of solutions for variational inequalities.
Numerische Mathematik
Cheon Seoung Ryoo, Mitsuhiro T. Nakao
1997 J jnl
Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case.
Reliab. Comput.
Teruya Minamoto, Mitsuhiro T. Nakao