Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case. - Teruya Minamoto; Mitsuhiro T. Nakao (Reliab. Comput., 1997)

Numerical verification of solutions for variational inequalities. - Cheon Seoung Ryoo; Mitsuhiro T. Nakao (Numerische Mathematik, 1998)

Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations. - Mitsuhiro T. Nakao; Nobito Yamamoto; Yoshitaka Watanabe (Reliab. Comput., 1998)

A Numerical Verification Method of Solutions for the Navier-Stokes Equations. - Yoshitaka Watanabe; Nobito Yamamoto; Mitsuhiro T. Nakao (Reliab. Comput., 1999)

A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Elements. - Mitsuhiro T. Nakao; Nobito Yamamoto (Perspectives on Enclosure Methods, 2001)

Some Computer Assisted Proofs for Solutions of the Heat Convection Problems. - Mitsuhiro T. Nakao; Yoshitaka Watanabe; Nobito Yamamoto; Takaaki Nishida (Reliab. Comput., 2003)

An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations. - Mitsuhiro T. Nakao; Yoshitaka Watanabe (Numer. Algorithms, 2004)

A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems. - Mitsuhiro T. Nakao; Kouji Hashimoto; Yoshitaka Watanabe (Computing, 2005)

SCAN'2004 11th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated NumericsFukuoka, Japan, October 4-8, 2004. - Mitsuhiro T. Nakao; Kaori Nagatou (Reliab. Comput., 2005)

Some remarks on the behaviour of the finite element solution in nonsmooth domains. - Mitsuhiro T. Nakao; Takehiko Kinoshita (Appl. Math. Lett., 2008)

On very accurate verification of solutions for boundary value problems by using spectral methods. - Mitsuhiro T. Nakao; Takehiko Kinoshita (JSIAM Lett., 2009)

A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. - Myoungnyoun Kim; Mitsuhiro T. Nakao; Yoshitaka Watanabe; Takaaki Nishida (Numerische Mathematik, 2009)

On very accurate enclosure of the optimal constant in the a priori error estimates for H20-projection. - Takehiko Kinoshita; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2010)

A numerical verification method for a periodic solution of a delay differential equation. - Teruya Minamoto; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2010)

Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems. - Mitsuhiro T. Nakao; Yoshitaka Watanabe; Nobito Yamamoto; Takaaki Nishida; Myoung-Nyoung Kim (J. Sci. Comput., 2010)

Erratum to: Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems. - Mitsuhiro T. Nakao; Yoshitaka Watanabe; Nobito Yamamoto; Takaaki Nishida; Myoungnyoun Kim (J. Sci. Comput., 2010)

A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations. - Takehiko Kinoshita; Takuma Kimura; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2011)

On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. - Mitsuhiro T. Nakao; Takehiko Kinoshita; Takuma Kimura (Computing, 2012)

Some Remarks on the Optimal Error Estimates for the Finite Element Method on the L-Shaped Domain. - Takehiko Kinoshita; Mitsuhiro T. Nakao (ITNG, 2013)

A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations. - Yoshitaka Watanabe; Takehiko Kinoshita; Mitsuhiro T. Nakao (Math. Comput., 2013)

Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation. - Mitsuhiro T. Nakao; Takuma Kimura; Takehiko Kinoshita (SIAM J. Numer. Anal., 2013)

Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators. - Takehiko Kinoshita; Yoshitaka Watanabe; Mitsuhiro T. Nakao (SCAN, 2014)

On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems. - Takehiko Kinoshita; Takuma Kimura; Mitsuhiro T. Nakao (Numerische Mathematik, 2014)

Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces. - Yoshitaka Watanabe; Kaori Nagatou; Michael Plum; Mitsuhiro T. Nakao (SIAM J. Numer. Anal., 2014)

H3 and H4 Regularities of the Poisson Equation on Polygonal Domains. - Takehiko Kinoshita; Yoshitaka Watanabe; Mitsuhiro T. Nakao (MACIS, 2015)

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. - Yoshitaka Watanabe; Mitsuhiro T. Nakao (Appl. Math. Comput., 2016)

On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations. - Yoshitaka Watanabe; Mitsuhiro T. Nakao; Kaori Nagatou (JSIAM Lett., 2017)

A new formulation for the numerical proof of the existence of solutions to elliptic problems. - Kouta Sekine; Mitsuhiro T. Nakao; Shin'ichi Oishi (CoRR, 2019)

Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations. - Xuefeng Liu; Mitsuhiro T. Nakao; Chun'guang You; Shin'ichi Oishi (CoRR, 2020)

Constructive error estimates for full discrete approximation of periodic solution for heat equation. - Takuma Kimura; Teruya Minamoto; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2020)

Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space. - Takehiko Kinoshita; Yoshitaka Watanabe; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2020)

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. - Kouta Sekine; Mitsuhiro T. Nakao; Shin'ichi Oishi (Numerische Mathematik, 2020)

Foreword. - Mitsuhiro T. Nakao; Takeshi Ogita; Siegfried M. Rump (J. Comput. Appl. Math., 2021)

Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation. - Makoto Mizuguchi; Mitsuhiro T. Nakao; Kouta Sekine; Shin'ichi Oishi (J. Sci. Comput., 2021)

Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation. - Takuma Kimura; Teruya Minamoto; Mitsuhiro T. Nakao (Comput. Methods Appl. Math., 2022)

Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains. - Xuefeng Liu; Mitsuhiro T. Nakao; Shin'ichi Oishi (Commun. Nonlinear Sci. Numer. Simul., 2022)

On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators. - Takehiko Kinoshita; Yoshitaka Watanabe; Mitsuhiro T. Nakao (Acta Cybern., 2022)

Inclusion method of optimal constant with quadratic convergence for H01-projection error estimates and its applications. - Takehiko Kinoshita; Yoshitaka Watanabe; Nobito Yamamoto; Mitsuhiro T. Nakao (J. Comput. Appl. Math., 2023)

Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces. - Yoshitaka Watanabe; Takehiko Kinoshita; Mitsuhiro T. Nakao (J. Sci. Comput., 2023)

Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method. - Takuma Kimura; Teruya Minamoto; Mitsuhiro T. Nakao (Comput. Math. Appl., 2025)