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研究成果 1993 2019

  • 198 引用
  • 8 h指数
  • 34 記事
  • 5 会議での発言
  • 1 コメント/討論
  • 1 Conference article
2019

A computer-assisted method for the diblock copolymer model

Cai, S. & Watanabe, Y., 7 1 2019, : : ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 99, 7, e201800125.

研究成果: ジャーナルへの寄稿記事

Copolymer
Block copolymers
Banach Fixed Point Theorem
Sobolev spaces
Compact Operator

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

Kinoshita, T., Watanabe, Y. & Nakao, M. T., 4 15 2019, : : Journal of Differential Equations. 266, 9, p. 5431-5447 17 p.

研究成果: ジャーナルへの寄稿記事

Hilbert spaces
Linear Operator
Mathematical operators
Hilbert space
Norm
Dual space
Elliptic Operator
Linear Operator
A Priori Error Estimates
Invertibility

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

Kinoshita, T., Watanabe, Y. & Nakao, M. T., 1 1 2019, (受理済み/印刷中) : : Journal of Computational and Applied Mathematics. 112561.

研究成果: ジャーナルへの寄稿記事

Hilbert spaces
Compact Operator
Resolvent
Mathematical operators
Hilbert space
2017

Validated constructive error estimations for biharmonic problems

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

研究成果: ジャーナルへの寄稿記事

Computer-assisted Proof
Biharmonic Problem
Biharmonic Equation
Computational Techniques
Error Estimation
2016
1 引用 (Scopus)
Computer-assisted Proof
Numerical Verification
Rounding error
Floating point
Steady-state Solution
3 引用 (Scopus)
Numerical Verification
Functional equation
Nonlinear Equations
Computer-assisted Proof
Iteration

H3 and H4 regularities of the poisson equation on polygonal domains

Kinoshita, T., Watanabe, Y. & Nakao, M. T., 1 1 2016, Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Kotsireas, I. S., Rump, S. M. & Yap, C. K. (版). Springer Verlag, p. 199-201 3 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 9582).

研究成果: 著書/レポートタイプへの貢献会議での発言

Poisson equation
Poisson's equation
Equality
Regularity
A Priori Error Estimates
2 引用 (Scopus)

Norm bound computation for inverses of linear operators in Hilbert spaces

Watanabe, Y., Nagatou, K., Plum, M. & Nakao, M. T., 4 5 2016, : : Journal of Differential Equations. 260, 7, p. 6363-6374 12 p.

研究成果: ジャーナルへの寄稿記事

Invertibility
Hilbert spaces
Enclosures
Partial differential equations
Linear Operator
1 引用 (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., 12 1 2016, : : Japan Journal of Industrial and Applied Mathematics. 33, 3, p. 629-636 8 p.

研究成果: ジャーナルへの寄稿記事

Regular Solution
Poisson equation
A Priori Estimates
Poisson's equation
A Priori Error Estimates
2 引用 (Scopus)

Some remarks on the rigorous estimation of inverse linear elliptic operators

Kinoshita, T., Watanabe, Y. & Nakao, M. T., 1 1 2016, Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. von Gudenberg, J. W., Tucker, W. & Nehmeier, M. (版). Springer Verlag, p. 225-235 11 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 9553).

研究成果: 著書/レポートタイプへの貢献会議での発言

Elliptic Operator
Partial differential equations
Linear Operator
Mathematical operators
Numerical methods
2015
3 引用 (Scopus)
Elliptic Operator
Nonlinear Problem
Eigenvalue
Approximate Solution
Computer program listings
4 引用 (Scopus)

Some considerations of the invertibility verifications for linear elliptic operators

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

研究成果: ジャーナルへの寄稿記事

Invertibility
Elliptic Operator
Linear Operator
A Priori Error Estimates
Computing
2014
7 引用 (Scopus)

Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

Watanabe, Y., Nagatou, K., Plum, M. & Nakao, M. T., 1 1 2014, : : SIAM Journal on Numerical Analysis. 52, 2, p. 975-992 18 p.

研究成果: ジャーナルへの寄稿記事

Hilbert spaces
Set theory
Eigenvalue Problem
Mathematical operators
Hilbert space
2013
8 引用 (Scopus)

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

Watanabe, Y., Kinoshita, T. & Nakao, M. T., 5 30 2013, : : Mathematics of Computation. 82, 283, p. 1543-1557 15 p.

研究成果: ジャーナルへの寄稿記事

A Posteriori Estimates
Linear partial differential equation
Elliptic Partial Differential Equations
Boundary value problems
Partial differential equations
2012
5 引用 (Scopus)

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

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

研究成果: ジャーナルへの寄稿記事

FitzHugh-Nagumo Equations
Numerical Verification
Sobolev spaces
FitzHugh-Nagumo
Schauder Fixed Point Theorem
2011
2 引用 (Scopus)

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

Yamamoto, N., Nakao, M. T. & Watanabe, Y., 12 1 2011, : : Numerical Functional Analysis and Optimization. 32, 11, p. 1190-1204 15 p.

研究成果: ジャーナルへの寄稿記事

Fixed-point Equation
Numerical Verification
Uniqueness of Solutions
Theorem
Banach Fixed Point Theorem
2010
2 引用 (Scopus)

Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems

Nakao, M. T., Watanabe, Y., Yamamoto, N., Nishida, T. & Kim, M. N., 6 1 2010, : : Journal of Scientific Computing. 43, 3, p. 388-401 14 p.

研究成果: ジャーナルへの寄稿記事

Computer-assisted Proof
Heat convection
Convection
Heat
Fluids

Erratum: Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems (J Sci Comput (10.1007/s10915-009-9303-3))

Nakao, M. T., Watanabe, Y., Yamamoto, N., Nishida, T. & Kim, M., 7 1 2010, : : Journal of Scientific Computing. 44, 1, 1 p.

研究成果: ジャーナルへの寄稿コメント/討論

Computer-assisted Proof
Heat convection
Convection
Heat
2009
9 引用 (Scopus)

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

Watanabe, Y., 1 15 2009, : : Journal of Computational and Applied Mathematics. 223, 2, p. 953-966 14 p.

研究成果: ジャーナルへの寄稿記事

Computer-assisted Proof
Numerical Verification
Rounding error
Floating point
Steady-state Solution
4 引用 (Scopus)
Numerical Verification
Elliptic Partial Differential Equations
Nonlinear equations
Boundary value problems
Partial differential equations
9 引用 (Scopus)

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

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

研究成果: ジャーナルへの寄稿記事

Numerical Verification
Rayleigh
Three-dimensional
Fluids
Computer-assisted Proof
1 引用 (Scopus)
Numerical Verification
Rayleigh
Elliptic Equations
Heat convection
Bifurcation Point

Spectral problem on 3-D photonic crystals

Nagatou, K., Brown, M., Kim, M., Watanabe, Y. & Wood, I., 11 26 2009, Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. p. 922-925 4 p. (AIP Conference Proceedings; 巻数 1168).

研究成果: 著書/レポートタイプへの貢献会議での発言

photonics
nanotechnology
Maxwell equation
crystals
optics
2008
13 引用 (Scopus)

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

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

研究成果: ジャーナルへの寄稿記事

Poiseuille Flow
Orr-Sommerfeld Equation
Computer-assisted Proof
Hydrodynamic Stability
Numerical Verification
2005
28 引用 (Scopus)

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

Nakao, M. T., Hashimoto, K. & Watanabe, Y., 7 1 2005, : : Computing (Vienna/New York). 75, 1 SPEC. ISS., p. 1-14 14 p.

研究成果: ジャーナルへの寄稿記事

Invertibility
Elliptic Operator
Linear Operator
Nonlinear Problem
Numerical methods

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

Hashimoto, K., Abe, R., Nakao, M. T. & Watanabe, Y., 2 2005, : : Japan Journal of Industrial and Applied Mathematics. 22, 1, p. 111-131 21 p.

研究成果: ジャーナルへの寄稿記事

Numerical Verification
A Priori Error Estimates
Singularly Perturbed Problem
Nonlinearity
Exponential Fitting

Performance comparison of vector-calculations between Itanium2 and other processors

Nanri, T., Watanabe, Y. & Sato, H., 12 1 2005, IWIA 2005: Innovative Architecture for Future Generation High-Performance Processors and Systems. 巻 2005. p. 141-146 6 p. 1587835

研究成果: 著書/レポートタイプへの貢献会議での発言

2004
15 引用 (Scopus)

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

Nakao, M. T. & Watanabe, Y., 12 1 2004, : : Numerical Algorithms. 37, 1-4 SPEC. ISS., p. 311-323 13 p.

研究成果: ジャーナルへの寄稿記事

Numerical Verification
Elliptic Differential Equations
Differential equations
Derivatives
Poisson equation
16 引用 (Scopus)

A numerical verification of nontrivial solutions for the heat convection problem

Watanabe, Y., Yamamoto, N., Nakao, M. T. & Nishida, T., 12 1 2004, : : Journal of Mathematical Fluid Mechanics. 6, 1, p. 1-20 20 p.

研究成果: ジャーナルへの寄稿記事

Computer-assisted Proof
Numerical Verification
Heat convection
Rounding error
Floating point
2003
7 引用 (Scopus)

Some computer assisted proofs for solutions of the heat convection problems

Nakao, M. T., Watanabe, Y., Yamamoto, N. & Nishida, T., 10 2003, : : Reliable Computing. 9, 5, p. 359-372 14 p.

研究成果: ジャーナルへの寄稿記事

Computer-assisted Proof
Heat convection
Nontrivial Solution
Convection
Heat
2002
4 引用 (Scopus)

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

Toyonaga, K., Nakao, M. T. & Watanabe, Y., 10 1 2002, : : Journal of Computational and Applied Mathematics. 147, 1, p. 175-190 16 p.

研究成果: ジャーナルへの寄稿記事

Multiple Eigenvalues
Elliptic Operator
Numerical Computation
Eigenvalue Problem
Mathematical operators
2001

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

Nakao, M. T., Watanabe, Y. & Yamamoto, N., 6 2001, : : Japan Journal of Industrial and Applied Mathematics. 18, 2, p. 587-602 16 p.

研究成果: ジャーナルへの寄稿記事

Enclosure
Enclosures
Elliptic Problems
Numerical Computation
Eigenvalue Problem
2000

Preliminary investigation of distributed shared memory system on a cluster of high performance clusters

Nanri, T., Watanabe, Y., Sato, H. & Shimasaki, M., 12 1 2000, European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000.

研究成果: 著書/レポートタイプへの貢献会議での発言

Distributed Shared Memory
High Performance
Data storage equipment
Computer systems
Runtime Systems
1999
10 引用 (Scopus)

A Numerical Verification Method of Solutions for the Navier-Stokes Equations

Watanabe, Y., Yamamoto, N. & Nakao, M. T., 1 1 1999, : : Reliable Computing. 5, 3, p. 347-357 11 p.

研究成果: ジャーナルへの寄稿Conference article

Numerical Verification
Navier Stokes equations
Navier-Stokes Equations
Stationary Navier-Stokes Equations
Fixed point theorem
1998
7 引用 (Scopus)

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

Nakao, M. T., Yamamoto, N. & Watanabe, Y., 4 24 1998, : : Journal of Computational and Applied Mathematics. 91, 1, p. 137-158 22 p.

研究成果: ジャーナルへの寄稿記事

A Priori Error Bounds
Stokes Equations
Finite Element Solution
Inf-sup Condition
Stokes Problem
1 引用 (Scopus)

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

Nakao, M. T., Yamamoto, N. & Watanabe, Y., 12 1 1998, : : Reliable Computing. 23, 5, p. 115-124 10 p.

研究成果: ジャーナルへの寄稿記事

Stokes Equations
Finite Element Solution
Error Bounds
Error Estimates
Rate of Convergence
1997
5 引用 (Scopus)

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

Watanabe, Y., Yamamoto, N. & Nakao, M. T., 2 3 1997, : : Nonlinear Analysis, Theory, Methods and Applications. 28, 3, p. 577-587 11 p.

研究成果: ジャーナルへの寄稿記事

Piecewise linear techniques
Magnetohydrodynamics
Elliptic Equations
Boundary value problems
Fixed point theorem
1994
4 引用 (Scopus)

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

Nakao, M. T. & Watanabe, Y., 5 20 1994, : : Journal of Computational and Applied Mathematics. 50, 1-3, p. 401-410 10 p.

研究成果: ジャーナルへの寄稿記事

Nonlinear Parabolic Problems
Numerical Verification
Existence of Solutions
Parabolic Problems
A Priori Error Estimates
1993
25 引用 (Scopus)

Numerical verifications of solutions for nonlinear elliptic equations

Watanabe, Y. & Nakao, M. T., 2 1 1993, : : Japan Journal of Industrial and Applied Mathematics. 10, 1, p. 165-178 14 p.

研究成果: ジャーナルへの寄稿記事

Nonlinear Elliptic Boundary Value Problem
Numerical Verification
Existence of Weak Solutions
Nonlinear Elliptic Equations
Finite Element Approximation