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## Nakao, Mitsuhiro T.

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 Author ID: nakao.mitsuhiro-t Published as: Nakao, M. T.; Nakao, Mitsuhiro; Nakao, Mitsuhiro T.; Tomonaga, Mitsuhiro Homepage: https://www2.math.kyushu-u.ac.jp/~mtnakao/profile.html External Links: dblp
 Documents Indexed: 123 Publications since 1981, including 3 Books
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#### Co-Authors

 33 single-authored 40 Watanabe, Yoshitaka 34 Yamamoto, Nobito 19 Kinoshita, Takehiko 10 Hashimoto, Kouji 10 Nagatou, Kaori 7 Kimura, Takuma 6 Minamoto, Teruya 6 Nishida, Takaaki 6 Ryoo, Cheon Seoung 5 Plum, Michael 3 Rump, Siegfried Michael 2 Kim, Myoungnyoun 2 Kobayashi, Kenta 2 Wakayama, Masato 1 Abe, Ryohei 1 Alefeld, Götz E. 1 Kearfott, Baker 1 Kim, Myoung-Nyoung 1 Kimura, Seiji 1 Lee, Sang Hun 1 Neumaier, Arnold 1 Ogita, Takeshi 1 Oishi, Shin’ichi 1 Sekine, Kouta 1 Sharyĭ, Sergeĭ Petrovich 1 Tsuchiya, Takuya 1 Van Hentenryck, Pascal
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#### Serials

 16 Journal of Computational and Applied Mathematics 12 RIMS Kokyuroku 10 Japan Journal of Industrial and Applied Mathematics 8 Numerical Functional Analysis and Optimization 6 Numerische Mathematik 4 Reliable Computing 3 Bulletin of the Kyushu Institute of Technology. Mathematics, Natural Science 3 Memoirs of the Faculty of Science. Series A. Mathematics 2 Computers & Mathematics with Applications 2 Journal of Mathematical Analysis and Applications 2 Mathematics of Computation 2 Computing 2 Journal of Differential Equations 2 Journal of Information Processing 2 SIAM Journal on Numerical Analysis 2 Japan Journal of Applied Mathematics 2 Journal of Scientific Computing 2 Sugaku Expositions 2 JSIAM Letters 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Computation 1 Hokkaido Mathematical Journal 1 Journal of Approximation Theory 1 Mathematica Japonica 1 Memoirs of Numerical Mathematics 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Sūgaku 1 Applied Mathematics Letters 1 Numerical Algorithms 1 Linear Algebra and its Applications 1 Methods and Applications of Analysis 1 Interval Computations 1 Vychislitel’nye Tekhnologii 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Mathematical Fluid Mechanics 1 Information 1 Springer Series in Computational Mathematics 1 Journal of Math-for-Industry 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 112 Numerical analysis (65-XX) 77 Partial differential equations (35-XX) 16 Fluid mechanics (76-XX) 13 Ordinary differential equations (34-XX) 10 Operator theory (47-XX) 7 Computer science (68-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 General and overarching topics; collections (00-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH

82 Publications have been cited 678 times in 252 Documents Cited by Year
A numerical approach to the proof of existence of solutions for elliptic problems. Zbl 0694.35051
Nakao, Mitsuhiro T.
1988
Numerical verification methods for solutions of ordinary and partial differential equations. Zbl 1106.65315
Nakao, Mitsuhiro T.
2001
A numerical verification method for the existence of weak solutions for nonlinear boundary value problems. Zbl 0771.65046
Nakao, Mitsuhiro T.
1992
Standardized notation in interval analysis. Zbl 1196.65088
Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P.
2010
Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element. Zbl 0832.65123
Yamamoto, Nobito; Nakao, Mitsuhiro T.
1995
A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. Zbl 1151.35337
Nakao, M. T.; Hashimoto, K.; Watanabe, Y.
2005
Solving nonlinear elliptic problems with result verification using an $$H^{-1}$$ type residual iteration. Zbl 0802.65111
Nakao, Mitsuhiro T.
1993
Numerical verification of solutions for nonlinear elliptic problems using an $$L^\infty$$ residual method. Zbl 0893.35006
Nakao, Mitsuhiro T.; Yamamoto, Nobito
1998
Numerical verifications of solutions for nonlinear elliptic equations. Zbl 0784.65082
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
1993
A numerical approach to the proof of existence of solutions for elliptic problems. II. Zbl 0717.35019
Nakao, Mitsuhiro T.
1990
On the best constant in the error bound for the $$H_0^1$$-projection into piecewise polynomial spaces. Zbl 0907.65100
Nakao, Mitsuhiro T.; Yamamoto, Nobito; Kimura, Seiji
1998
Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains. Zbl 0797.65081
Yamamoto, Nobito; Nakao, Mitsuhiro T.
1993
An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness. Zbl 0938.65137
Nagatou, K.; Yamamoto, N.; Nakao, M. T.
1999
Numerical verification of solutions for variational inequalities. Zbl 0919.65043
Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.
1998
Superconvergence of the gradient of Galerkin approximations for elliptic problems. Zbl 0642.65072
Nakao, Mitsuhiro T.
1987
Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension. Zbl 0575.65112
Nakao, Mitsuhiro T.
1985
A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Zbl 1156.76025
Watanabe, Yoshitaka; Plum, Michael; Nakao, Mitsuhiro T.
2009
An efficient approach to the numerical verification for solutions of elliptic differential equations. Zbl 1114.65152
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
2004
A numerical verification of nontrivial solutions for the heat convection problem. Zbl 1062.35092
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.; Nishida, Takaaki
2004
A guaranteed bound of the optimal constant in the error estimates for linear triangular element. Zbl 1013.65119
Nakao, M. T.; Yamamoto, N.
2001
Numerical verifications for eigenvalues of second-order elliptic operators. Zbl 1306.65278
Nakao, M. T.; Yamamoto, N.; Nagatou, K.
1999
Verified numerical computations for eigenvalues of non-commutative harmonic oscillators. Zbl 1016.65056
Nagatou, K.; Nakao, M. T.; Wakayama, M.
2002
Solving nonlinear parabolic problems with result verification. I: One- space dimensional case. Zbl 0744.65065
Nakao, Mitsuhiro T.
1991
Constructive a priori error estimates for a full discrete approximation of the heat equation. Zbl 1293.65121
Nakao, Mitsuhiro T.; Kimura, Takuma; Kinoshita, Takehiko
2013
A numerical verification method for a periodic solution of a delay differential equation. Zbl 1202.65086
Minamoto, Teruya; Nakao, Mitsuhiro T.
2010
A guaranteed bound of the optimal constant in the error estimates for linear triangular elements. II: Details. Zbl 0990.65123
Nakao, Mitsuhiro T.; Yamamoto, Nobito
2001
A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations. Zbl 1280.65119
Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2013
Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. Zbl 1294.35047
Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2014
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. Zbl 1246.65173
Nakao, Mitsuhiro T.; Kinoshita, Takehiko; Kimura, Takuma
2012
A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. Zbl 1155.76024
Kim, Myoungnyoun; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Nishida, Takaaki
2009
Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications. Zbl 1154.65081
Nakao, Mitsuhiro T.; Hashimoto, Kouji
2008
Numerical verification of stationary solutions for Navier-Stokes problems. Zbl 1106.76057
Nagatou, K.; Hashimoto, K.; Nakao, M. T.
2007
Numerical verification of solutions for elasto-plastic torsion problems. Zbl 0979.74022
Nakao, M. T.; Lee, S. H.; Ryoo, Cheon Seoung
2000
Superconvergence of the gradient of Galerkin approximations for elliptic problems. Zbl 0642.65073
Nakao, Mitsuhiro T.
1987
Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation. Zbl 1115.65118
Minamoto, Teruya; Nakao, Mitsuhiro T.
2007
Some computer assisted proofs for solutions of the heat convection problems. Zbl 1126.35352
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki
2003
Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points. Zbl 0890.34013
Tsuchiya, Takuya; Nakao, Mitsuhiro T.
1997
Numerical verifications of solutions for elliptic equations with strong nonlinearity. Zbl 0746.35014
Nakao, Mitsuhiro T.; Yamamoto, Nobito
1991
Norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 1398.65094
Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2016
Some considerations of the invertibility verifications for linear elliptic operators. Zbl 1320.35164
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Kinoshita, Takehiko; Kimura, Takuma; Yamamoto, Nobito
2015
On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems. Zbl 1293.35062
Kinoshita, Takehiko; Kimura, Takuma; Nakao, Mitsuhiro T.
2014
Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Zbl 1364.34124
Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2012
A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations. Zbl 1236.65101
Kinoshita, T.; Kimura, T.; Nakao, M. T.
2011
A numerical verification method for solutions of nonlinear parabolic problems. Zbl 1211.35153
Nakao, Mitsuhiro T.; Hashimoto, Kouji
2009
On the $$L^{2}$$ a priori error estimates to the finite element solution of elliptic problems with singular adjoint operator. Zbl 1165.35009
Kinoshita, T.; Hashimoto, K.; Nakao, M. T.
2009
Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains. Zbl 1134.76029
Nakao, Mitsuhiro T.; Hashimoto, Koiji; Kobayashi, Kenta
2007
A numerical verification method of solutions for the Navier-Stokes equations. Zbl 0947.65121
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1999
A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations. Zbl 0930.65122
Nakao, Mitsuhiro T.; Yamamoto, Nobito; Watanabe, Yoshitaka
1998
Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case. Zbl 0886.65098
Minamoto, Teruya; Nakao, Mitsuhiro T.
1997
Verified computations of solutions for nondifferentiable elliptic equations related to MHD equilibria. Zbl 0864.35089
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1997
Numerical verification methods and computer-assisted proofs for partial differential equations. Zbl 07063008
Nakao, Mitsuhiro T.; Plum, Michael; Watanabe, Yoshitaka
2019
Some remarks on the rigorous estimation of inverse linear elliptic operators. Zbl 1354.65232
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. Zbl 1203.80010
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoung-Nyoung
2010
Some remarks on the behaviour of the finite element solution in nonsmooth domains. Zbl 1184.35120
Nakao, Mitsuhiro T.; Kinoshita, Takehiko
2008
Numerical verification method for solutions of the perturbed Gelfand equation. Zbl 1002.65122
Minamoto, Teruya; Yamamoto, Nobito; Nakao, Mitsuhiro T.
2000
Numerical verifications of solutions for nonlinear hyperbolic equations. Zbl 0834.65095
Nakao, Mitsuhiro T.
1994
On computational proofs of the existence of solutions to nonlinear parabolic problems. Zbl 0806.65098
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
1994
Computable $$L^ \infty$$ error estimates in the finite element method with applications to nonlinear elliptic problems. Zbl 0834.65101
Nakao, Mitsuhiro T.
1993
$$L^{\infty}$$ error estimates and superconvergence results for a collocation-$$H^{-1}$$-Galerkin method for elliptic equations. Zbl 0584.65073
Nakao, Mitsuhiro T.
1985
Some superconvergence estimates for a Galerkin method for elliptic problems. Zbl 0575.65105
Nakao, Mitsuhiro
1984
An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space. Zbl 07094577
Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2019
An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 07041840
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2019
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. Zbl 1410.65228
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
A theorem for numerical verification on local uniqueness of solutions to fixed-point equations. Zbl 1232.47059
Yamamoto, Nobito; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
2011
On very accurate enclosure of the optimal constant in the a priori error estimates for $$H_0^2$$-projection. Zbl 1190.65166
Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2010
Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. Zbl 1184.65106
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2009
Numerical verification of solutions for obstacle problems. Zbl 1041.65056
Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.
2003
An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems. Zbl 0976.65096
Nagatou, K.; Nakao, M. T.
2001
Validated computation for a linear elliptic problem with a parameter. Zbl 0953.65080
Yamamoto, Nobito; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
1999
Some superconvergence of Galerkin approximations for parabolic and hyperbolic problems in one space dimension. Zbl 0623.65119
Nakao, Mitsuhiro T.
1985
Constructive error estimates for full discrete approximation of periodic solution for heat equation. Zbl 1440.65141
Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.
2020
Constructive error analysis of a full-discrete finite element method for the heat equation. Zbl 1427.65216
Hashimoto, Kouji; Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.
2019
Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains. Zbl 1367.65152
Kinoshita, Takehiko; Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
2016
$$H^3$$ and $$H^4$$ regularities of the Poisson equation on polygonal domains. Zbl 06585024
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
Erratum to: Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. Zbl 1203.80011
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoungnyoun
2010
Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004). Selected papers based on the presentations at the 11th GAMM-IMACS international symposium, Fukuoka, Japan, October 4–8, 2004. Zbl 1127.68306
Alefeld, Götz (ed.); Nakao, Mitsuhiro (ed.); Rump, Siegfried M. (ed.)
2007
Numerical verification of solutions for variational inequalities of the second kind. Zbl 1010.65030
Ryoo, C. S.; Nakao, M. T.
2002
Solutions with guaranteed accuracy for coupling-type eigenvalue problems related to noncommutative harmonic oscillators. Zbl 0968.65519
Nagatou, Kaori; Nakao, Mitsuhiro T.; Wakayama, Masato
2000
A numerical verification method of solutions for the Navier-Stokes equations. Zbl 0971.76050
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1999
State of the art for numerical computations with guaranteed accuracy. Zbl 0916.65044
Nakao, Mitsuhiro T.
1998
Superconvergence estimates at Jacobi points of the collocation-Galerkin method for two point boundary value problems. Zbl 0575.65078
Nakao, Mitsuhiro
1984
Some superconvergence estimates for a collocation-$$H^{-1}$$-Galerkin method for parabolic problems. Zbl 0497.65058
Nakao, Mitsuhiro
1981
Constructive error estimates for full discrete approximation of periodic solution for heat equation. Zbl 1440.65141
Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.
2020
Numerical verification methods and computer-assisted proofs for partial differential equations. Zbl 07063008
Nakao, Mitsuhiro T.; Plum, Michael; Watanabe, Yoshitaka
2019
An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space. Zbl 07094577
Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2019
An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 07041840
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2019
Constructive error analysis of a full-discrete finite element method for the heat equation. Zbl 1427.65216
Hashimoto, Kouji; Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.
2019
Norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 1398.65094
Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2016
Some remarks on the rigorous estimation of inverse linear elliptic operators. Zbl 1354.65232
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. Zbl 1410.65228
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains. Zbl 1367.65152
Kinoshita, Takehiko; Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
2016
$$H^3$$ and $$H^4$$ regularities of the Poisson equation on polygonal domains. Zbl 06585024
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2016
Some considerations of the invertibility verifications for linear elliptic operators. Zbl 1320.35164
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Kinoshita, Takehiko; Kimura, Takuma; Yamamoto, Nobito
2015
Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. Zbl 1294.35047
Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2014
On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems. Zbl 1293.35062
Kinoshita, Takehiko; Kimura, Takuma; Nakao, Mitsuhiro T.
2014
Constructive a priori error estimates for a full discrete approximation of the heat equation. Zbl 1293.65121
Nakao, Mitsuhiro T.; Kimura, Takuma; Kinoshita, Takehiko
2013
A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations. Zbl 1280.65119
Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2013
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. Zbl 1246.65173
Nakao, Mitsuhiro T.; Kinoshita, Takehiko; Kimura, Takuma
2012
Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Zbl 1364.34124
Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.
2012
A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations. Zbl 1236.65101
Kinoshita, T.; Kimura, T.; Nakao, M. T.
2011
A theorem for numerical verification on local uniqueness of solutions to fixed-point equations. Zbl 1232.47059
Yamamoto, Nobito; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
2011
Standardized notation in interval analysis. Zbl 1196.65088
Kearfott, R. B.; Nakao, M. T.; Neumaier, A.; Rump, S. M.; Shary, S. P.; van Hentenryck, P.
2010
A numerical verification method for a periodic solution of a delay differential equation. Zbl 1202.65086
Minamoto, Teruya; Nakao, Mitsuhiro T.
2010
Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. Zbl 1203.80010
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoung-Nyoung
2010
On very accurate enclosure of the optimal constant in the a priori error estimates for $$H_0^2$$-projection. Zbl 1190.65166
Kinoshita, Takehiko; Nakao, Mitsuhiro T.
2010
Erratum to: Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. Zbl 1203.80011
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoungnyoun
2010
A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Zbl 1156.76025
Watanabe, Yoshitaka; Plum, Michael; Nakao, Mitsuhiro T.
2009
A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. Zbl 1155.76024
Kim, Myoungnyoun; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Nishida, Takaaki
2009
A numerical verification method for solutions of nonlinear parabolic problems. Zbl 1211.35153
Nakao, Mitsuhiro T.; Hashimoto, Kouji
2009
On the $$L^{2}$$ a priori error estimates to the finite element solution of elliptic problems with singular adjoint operator. Zbl 1165.35009
Kinoshita, T.; Hashimoto, K.; Nakao, M. T.
2009
Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. Zbl 1184.65106
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
2009
Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications. Zbl 1154.65081
Nakao, Mitsuhiro T.; Hashimoto, Kouji
2008
Some remarks on the behaviour of the finite element solution in nonsmooth domains. Zbl 1184.35120
Nakao, Mitsuhiro T.; Kinoshita, Takehiko
2008
Numerical verification of stationary solutions for Navier-Stokes problems. Zbl 1106.76057
Nagatou, K.; Hashimoto, K.; Nakao, M. T.
2007
Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation. Zbl 1115.65118
Minamoto, Teruya; Nakao, Mitsuhiro T.
2007
Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains. Zbl 1134.76029
Nakao, Mitsuhiro T.; Hashimoto, Koiji; Kobayashi, Kenta
2007
Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004). Selected papers based on the presentations at the 11th GAMM-IMACS international symposium, Fukuoka, Japan, October 4–8, 2004. Zbl 1127.68306
Alefeld, Götz (ed.); Nakao, Mitsuhiro (ed.); Rump, Siegfried M. (ed.)
2007
A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. Zbl 1151.35337
Nakao, M. T.; Hashimoto, K.; Watanabe, Y.
2005
An efficient approach to the numerical verification for solutions of elliptic differential equations. Zbl 1114.65152
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
2004
A numerical verification of nontrivial solutions for the heat convection problem. Zbl 1062.35092
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.; Nishida, Takaaki
2004
Some computer assisted proofs for solutions of the heat convection problems. Zbl 1126.35352
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki
2003
Numerical verification of solutions for obstacle problems. Zbl 1041.65056
Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.
2003
Verified numerical computations for eigenvalues of non-commutative harmonic oscillators. Zbl 1016.65056
Nagatou, K.; Nakao, M. T.; Wakayama, M.
2002
Numerical verification of solutions for variational inequalities of the second kind. Zbl 1010.65030
Ryoo, C. S.; Nakao, M. T.
2002
Numerical verification methods for solutions of ordinary and partial differential equations. Zbl 1106.65315
Nakao, Mitsuhiro T.
2001
A guaranteed bound of the optimal constant in the error estimates for linear triangular element. Zbl 1013.65119
Nakao, M. T.; Yamamoto, N.
2001
A guaranteed bound of the optimal constant in the error estimates for linear triangular elements. II: Details. Zbl 0990.65123
Nakao, Mitsuhiro T.; Yamamoto, Nobito
2001
An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems. Zbl 0976.65096
Nagatou, K.; Nakao, M. T.
2001
Numerical verification of solutions for elasto-plastic torsion problems. Zbl 0979.74022
Nakao, M. T.; Lee, S. H.; Ryoo, Cheon Seoung
2000
Numerical verification method for solutions of the perturbed Gelfand equation. Zbl 1002.65122
Minamoto, Teruya; Yamamoto, Nobito; Nakao, Mitsuhiro T.
2000
Solutions with guaranteed accuracy for coupling-type eigenvalue problems related to noncommutative harmonic oscillators. Zbl 0968.65519
Nagatou, Kaori; Nakao, Mitsuhiro T.; Wakayama, Masato
2000
An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness. Zbl 0938.65137
Nagatou, K.; Yamamoto, N.; Nakao, M. T.
1999
Numerical verifications for eigenvalues of second-order elliptic operators. Zbl 1306.65278
Nakao, M. T.; Yamamoto, N.; Nagatou, K.
1999
A numerical verification method of solutions for the Navier-Stokes equations. Zbl 0947.65121
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1999
Validated computation for a linear elliptic problem with a parameter. Zbl 0953.65080
Yamamoto, Nobito; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
1999
A numerical verification method of solutions for the Navier-Stokes equations. Zbl 0971.76050
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1999
Numerical verification of solutions for nonlinear elliptic problems using an $$L^\infty$$ residual method. Zbl 0893.35006
Nakao, Mitsuhiro T.; Yamamoto, Nobito
1998
On the best constant in the error bound for the $$H_0^1$$-projection into piecewise polynomial spaces. Zbl 0907.65100
Nakao, Mitsuhiro T.; Yamamoto, Nobito; Kimura, Seiji
1998
Numerical verification of solutions for variational inequalities. Zbl 0919.65043
Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.
1998
A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations. Zbl 0930.65122
Nakao, Mitsuhiro T.; Yamamoto, Nobito; Watanabe, Yoshitaka
1998
State of the art for numerical computations with guaranteed accuracy. Zbl 0916.65044
Nakao, Mitsuhiro T.
1998
Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points. Zbl 0890.34013
Tsuchiya, Takuya; Nakao, Mitsuhiro T.
1997
Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case. Zbl 0886.65098
Minamoto, Teruya; Nakao, Mitsuhiro T.
1997
Verified computations of solutions for nondifferentiable elliptic equations related to MHD equilibria. Zbl 0864.35089
Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.
1997
Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element. Zbl 0832.65123
Yamamoto, Nobito; Nakao, Mitsuhiro T.
1995
Numerical verifications of solutions for nonlinear hyperbolic equations. Zbl 0834.65095
Nakao, Mitsuhiro T.
1994
On computational proofs of the existence of solutions to nonlinear parabolic problems. Zbl 0806.65098
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka
1994
Solving nonlinear elliptic problems with result verification using an $$H^{-1}$$ type residual iteration. Zbl 0802.65111
Nakao, Mitsuhiro T.
1993
Numerical verifications of solutions for nonlinear elliptic equations. Zbl 0784.65082
Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
1993
Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains. Zbl 0797.65081
Yamamoto, Nobito; Nakao, Mitsuhiro T.
1993
Computable $$L^ \infty$$ error estimates in the finite element method with applications to nonlinear elliptic problems. Zbl 0834.65101
Nakao, Mitsuhiro T.
1993
A numerical verification method for the existence of weak solutions for nonlinear boundary value problems. Zbl 0771.65046
Nakao, Mitsuhiro T.
1992
Solving nonlinear parabolic problems with result verification. I: One- space dimensional case. Zbl 0744.65065
Nakao, Mitsuhiro T.
1991
Numerical verifications of solutions for elliptic equations with strong nonlinearity. Zbl 0746.35014
Nakao, Mitsuhiro T.; Yamamoto, Nobito
1991
A numerical approach to the proof of existence of solutions for elliptic problems. II. Zbl 0717.35019
Nakao, Mitsuhiro T.
1990
A numerical approach to the proof of existence of solutions for elliptic problems. Zbl 0694.35051
Nakao, Mitsuhiro T.
1988
Superconvergence of the gradient of Galerkin approximations for elliptic problems. Zbl 0642.65072
Nakao, Mitsuhiro T.
1987
Superconvergence of the gradient of Galerkin approximations for elliptic problems. Zbl 0642.65073
Nakao, Mitsuhiro T.
1987
Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension. Zbl 0575.65112
Nakao, Mitsuhiro T.
1985
$$L^{\infty}$$ error estimates and superconvergence results for a collocation-$$H^{-1}$$-Galerkin method for elliptic equations. Zbl 0584.65073
Nakao, Mitsuhiro T.
1985
Some superconvergence of Galerkin approximations for parabolic and hyperbolic problems in one space dimension. Zbl 0623.65119
Nakao, Mitsuhiro T.
1985
Some superconvergence estimates for a Galerkin method for elliptic problems. Zbl 0575.65105
Nakao, Mitsuhiro
1984
Superconvergence estimates at Jacobi points of the collocation-Galerkin method for two point boundary value problems. Zbl 0575.65078
Nakao, Mitsuhiro
1984
Some superconvergence estimates for a collocation-$$H^{-1}$$-Galerkin method for parabolic problems. Zbl 0497.65058
Nakao, Mitsuhiro
1981
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#### Cited by 209 Authors

 57 Nakao, Mitsuhiro T. 26 Watanabe, Yoshitaka 18 Yamamoto, Nobito 16 Lessard, Jean-Philippe 15 Ryoo, Cheon Seoung 14 Kinoshita, Takehiko 11 Li, Zi-Cai 11 Minamoto, Teruya 11 Nagatou, Kaori 11 Oishi, Shin’ichi 9 Hashimoto, Kouji 7 Liu, Xuefeng 7 Plum, Michael 7 Sharyĭ, Sergeĭ Petrovich 6 Huang, Hung-Tsai 6 Kimura, Takuma 6 Mizuguchi, Makoto 6 Ohm, Mi-Ray 6 Shin, Jun Yong 6 Tanaka, Kazuaki 5 Kawanago, Tadashi 5 Parmeggiani, Alberto 5 Rump, Siegfried Michael 5 Sekine, Kouta 5 Wakayama, Masato 4 Castelli, Roberto 4 Gameiro, Marcio F. 4 Hashemi, Behnam 4 James, J. D. Mireles 4 Neumaier, Arnold 4 Takayasu, Akitoshi 4 Wanner, Thomas 3 Babuška, Ivo 3 Chen, Xiaojun 3 Frommer, Andreas 3 Nishida, Takaaki 3 Ohura, Ryuji 3 Strouboulis, Theofanis 3 Upadhyay, Chandra Shekhar 3 Yan, Ningning 3 Zhang, Zhimin 2 Alefeld, Götz E. 2 Arioli, Gianni 2 Blömker, Dirk 2 Cai, Shuting 2 Calleja, Renato C. 2 Cyranka, Jacek 2 de la Llave, Rafael 2 Dehghan Takht Fooladi, Mehdi 2 Domes, Ferenc 2 Fang, Qing 2 Fernandez Hernandez, Jose 2 Gangaraj, S. K. 2 Gazdag-Tóth, Boglárka 2 Ichinose, Takashi 2 Kikuchi, Fumio 2 Kobayashi, Kenta 2 Křížek, Michal 2 Kubica, Bartłomiej Jacek 2 Kubo, Takayuki 2 Lee, Hyun Young 2 Lee, Sang Hun 2 Li, Zicai 2 Lin, Qun 2 Lin, Yanping 2 McKenna, Patrick Joseph 2 Mireles-James, Jason D. 2 Mischaikow, Konstantin 2 Nolde, Christian 2 Pelegrín, Blas 2 Reinhardt, Christian 2 Sander, Evelyn 2 Sharaya, Irene Aleksandrovna 2 Shi, Dongyang 2 van den Berg, Jan Bouwe 2 Xie, Hehu 2 Zhu, Jianzhong 1 Abe, Ryohei 1 Akhmerov, Ramil R. 1 Argyros, Ioannis Konstantinos 1 Balázs, István 1 Birrell, Jeremiah 1 Breden, Maxime 1 Breuer, B. 1 Capdeboscq, Yves 1 Celletti, Alessandra 1 Chekroun, Mickaël D. 1 Corsi, Livia 1 Courtois, Julien 1 Dahne, Joel 1 Dudás, János 1 Endo, Yasunori 1 Fang, Zhichao 1 Figueras, Jordi-Lluís 1 Fila, Marek 1 Filo, Ján 1 Fogelklou, Oswald 1 García-Azpeitia, Carlos 1 Garrione, Maurizio 1 Genma, Kenta ...and 109 more Authors
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#### Cited in 79 Serials

 46 Journal of Computational and Applied Mathematics 24 Japan Journal of Industrial and Applied Mathematics 10 Computers & Mathematics with Applications 10 Numerical Functional Analysis and Optimization 9 Journal of Differential Equations 8 Journal of Mathematical Analysis and Applications 8 Applied Mathematics and Computation 8 Numerische Mathematik 7 Linear Algebra and its Applications 6 Applied Mathematics Letters 5 Computer Methods in Applied Mechanics and Engineering 5 Applied Numerical Mathematics 4 Reliable Computing 4 Journal of Computational Dynamics 3 Mathematics of Computation 3 Computing 3 Mathematical and Computer Modelling 3 Engineering Analysis with Boundary Elements 3 Journal of Inequalities and Applications 3 SIAM Journal on Applied Dynamical Systems 3 JSIAM Letters 2 Communications in Mathematical Physics 2 Nonlinearity 2 BIT 2 SIAM Journal on Numerical Analysis 2 Acta Applicandae Mathematicae 2 Numerical Methods for Partial Differential Equations 2 Journal of Scientific Computing 2 Journal of Global Optimization 2 Numerical Algorithms 2 SIAM Journal on Mathematical Analysis 2 Journal of Dynamics and Differential Equations 2 Indagationes Mathematicae. New Series 2 International Journal of Wavelets, Multiresolution and Information Processing 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 2 East Asian Mathematical Journal 1 Archive for Rational Mechanics and Analysis 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Reports on Mathematical Physics 1 Czechoslovak Mathematical Journal 1 Journal of Approximation Theory 1 Journal of Optimization Theory and Applications 1 Proceedings of the Japan Academy. Series A 1 Applied Mathematics and Mechanics. (English Edition) 1 Chinese Annals of Mathematics. Series B 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Japan Journal of Applied Mathematics 1 Computers & Operations Research 1 Forum Mathematicum 1 Sugaku Expositions 1 Applications of Mathematics 1 Aequationes Mathematicae 1 Automation and Remote Control 1 European Journal of Operational Research 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Mathematical Programming. Series A. Series B 1 Foundations of Computing and Decision Sciences 1 Journal of Computer and Systems Sciences International 1 SIAM Journal on Scientific Computing 1 Discrete and Continuous Dynamical Systems 1 Constraints 1 Differential Equations and Dynamical Systems 1 Communications in Nonlinear Science and Numerical Simulation 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics 1 Journal of Applied Mathematics and Computing 1 Milan Journal of Mathematics 1 Boundary Value Problems 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Mathematics in Computer Science 1 Optimization Letters 1 The Annals of Applied Statistics 1 Advances in Numerical Analysis 1 International Journal of Numerical Methods and Applications 1 Journal of Applied Mathematics & Informatics 1 S$$\vec{\text{e}}$$MA Journal 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Cited in 29 Fields

 196 Numerical analysis (65-XX) 134 Partial differential equations (35-XX) 36 Ordinary differential equations (34-XX) 29 Operator theory (47-XX) 18 Dynamical systems and ergodic theory (37-XX) 16 Mechanics of deformable solids (74-XX) 14 Operations research, mathematical programming (90-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Computer science (68-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Fluid mechanics (76-XX) 7 Quantum theory (81-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Functional analysis (46-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)