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Research Output

  • 209 Citations
  • 9 h-Index
  • 35 Article
  • 5 Conference contribution
  • 1 Comment/debate
  • 1 Conference article
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Article
2020

Some improvements of invertibility verifications for second-order linear elliptic operators

Watanabe, Y., Kinoshita, T. & Nakao, M. T., Aug 2020, In : Applied Numerical Mathematics. 154, p. 36-46 11 p.

Research output: Contribution to journalArticle

2019

A computer-assisted method for the diblock copolymer model

Cai, S. & Watanabe, Y., Jul 2019, In : ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 99, 7, e201800125.

Research output: Contribution to journalArticle

An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

Kinoshita, T., Watanabe, Y. & Nakao, M. T., Apr 15 2019, In : Journal of Differential Equations. 266, 9, p. 5431-5447 17 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
1 Citation (Scopus)

Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space

Kinoshita, T., Watanabe, Y. & Nakao, M. T., Jan 1 2019, (Accepted/In press) In : Journal of Computational and Applied Mathematics. 112561.

Research output: Contribution to journalArticle

2017

Validated constructive error estimations for biharmonic problems

Kinoshita, T., Watanabe, Y. & Nakao, M. T., Jan 1 2017, In : Reliable Computing. 25, p. 168-177 10 p.

Research output: Contribution to journalArticle

2016
1 Citation (Scopus)
4 Citations (Scopus)

Norm bound computation for inverses of linear operators in Hilbert spaces

Watanabe, Y., Nagatou, K., Plum, M. & Nakao, M. T., Apr 5 2016, In : Journal of Differential Equations. 260, 7, p. 6363-6374 12 p.

Research output: Contribution to journalArticle

3 Citations (Scopus)

Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains

Kinoshita, T., Watanabe, Y., Yamamoto, N. & Nakao, M. T., Dec 1 2016, In : Japan Journal of Industrial and Applied Mathematics. 33, 3, p. 629-636 8 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
2015
3 Citations (Scopus)

Some considerations of the invertibility verifications for linear elliptic operators

Nakao, M. T., Watanabe, Y., Kinoshita, T., Kimura, T. & Yamamoto, N., Jan 1 2015, In : Japan Journal of Industrial and Applied Mathematics. 32, 1, p. 19-31 13 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)
2014

Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

Watanabe, Y., Nagatou, K., Plum, M. & Nakao, M. T., 2014, In : SIAM Journal on Numerical Analysis. 52, 2, p. 975-992 18 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)
2013

A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

Watanabe, Y., Kinoshita, T. & Nakao, M. T., May 30 2013, In : Mathematics of Computation. 82, 283, p. 1543-1557 15 p.

Research output: Contribution to journalArticle

9 Citations (Scopus)
2012

A numerical verification method for a system of FitzHugh-Nagumo type

Cai, S., Nagatou, K. & Watanabe, Y., Oct 1 2012, In : Numerical Functional Analysis and Optimization. 33, 10, p. 1195-1220 26 p.

Research output: Contribution to journalArticle

6 Citations (Scopus)
2011

A theorem for numerical verification on local uniqueness of solutions to fixed-point equations

Yamamoto, N., Nakao, M. T. & Watanabe, Y., Dec 1 2011, In : Numerical Functional Analysis and Optimization. 32, 11, p. 1190-1204 15 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2010

Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems

Nakao, M. T., Watanabe, Y., Yamamoto, N., Nishida, T. & Kim, M. N., Jun 1 2010, In : Journal of Scientific Computing. 43, 3, p. 388-401 14 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2009

A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid

Watanabe, Y., Jan 15 2009, In : Journal of Computational and Applied Mathematics. 223, 2, p. 953-966 14 p.

Research output: Contribution to journalArticle

9 Citations (Scopus)
4 Citations (Scopus)

A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems

Kim, M., Nakao, M. T., Watanabe, Y. & Nishida, T., Jan 1 2009, In : Numerische Mathematik. 111, 3, p. 389-406 18 p.

Research output: Contribution to journalArticle

9 Citations (Scopus)
1 Citation (Scopus)
2008

A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Watanabe, Y., Plum, M. & Nakao, M. T., Jan 1 2008, In : ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 89, 1, p. 5-18 14 p.

Research output: Contribution to journalArticle

13 Citations (Scopus)
2005

A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems

Nakao, M. T., Hashimoto, K. & Watanabe, Y., Jul 1 2005, In : Computing (Vienna/New York). 75, 1 SPEC. ISS., p. 1-14 14 p.

Research output: Contribution to journalArticle

29 Citations (Scopus)

A numerical verification method for solutions of singularly perturbed problems with nonlinearity

Hashimoto, K., Abe, R., Nakao, M. T. & Watanabe, Y., Feb 2005, In : Japan Journal of Industrial and Applied Mathematics. 22, 1, p. 111-131 21 p.

Research output: Contribution to journalArticle

2004

An efficient approach to the numerical verification for solutions of elliptic differential equations

Nakao, M. T. & Watanabe, Y., Dec 1 2004, In : Numerical Algorithms. 37, 1-4 SPEC. ISS., p. 311-323 13 p.

Research output: Contribution to journalArticle

15 Citations (Scopus)

A numerical verification of nontrivial solutions for the heat convection problem

Watanabe, Y., Yamamoto, N., Nakao, M. T. & Nishida, T., Dec 1 2004, In : Journal of Mathematical Fluid Mechanics. 6, 1, p. 1-20 20 p.

Research output: Contribution to journalArticle

17 Citations (Scopus)
2003

Some computer assisted proofs for solutions of the heat convection problems

Nakao, M. T., Watanabe, Y., Yamamoto, N. & Nishida, T., Oct 2003, In : Reliable Computing. 9, 5, p. 359-372 14 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)
2002

Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators

Toyonaga, K., Nakao, M. T. & Watanabe, Y., Oct 1 2002, In : Journal of Computational and Applied Mathematics. 147, 1, p. 175-190 16 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)
2001

Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data

Nakao, M. T., Watanabe, Y. & Yamamoto, N., Jun 2001, In : Japan Journal of Industrial and Applied Mathematics. 18, 2, p. 587-602 16 p.

Research output: Contribution to journalArticle

1998

A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations

Nakao, M. T., Yamamoto, N. & Watanabe, Y., Apr 24 1998, In : Journal of Computational and Applied Mathematics. 91, 1, p. 137-158 22 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)

Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations

Nakao, M. T., Yamamoto, N. & Watanabe, Y., Dec 1 1998, In : Reliable Computing. 23, 5, p. 115-124 10 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
1997

Verified computations of solutions for nondifferentiable elliptic equations related to MHD equilibria

Watanabe, Y., Yamamoto, N. & Nakao, M. T., Feb 3 1997, In : Nonlinear Analysis, Theory, Methods and Applications. 28, 3, p. 577-587 11 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)
1994

On computational proofs of the existence of solutions to nonlinear parabolic problems

Nakao, M. T. & Watanabe, Y., May 20 1994, In : Journal of Computational and Applied Mathematics. 50, 1-3, p. 401-410 10 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)
1993

Numerical verifications of solutions for nonlinear elliptic equations

Watanabe, Y. & Nakao, M. T., Feb 1 1993, In : Japan Journal of Industrial and Applied Mathematics. 10, 1, p. 165-178 14 p.

Research output: Contribution to journalArticle

25 Citations (Scopus)