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Research Output 1993 2019

  • 194 Citations
  • 8 h-Index
  • 33 Article
  • 5 Conference contribution
  • 1 Comment/debate
  • 1 Conference article
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Article
2019

A computer-assisted method for the diblock copolymer model

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

Research output: Contribution to journalArticle

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., Apr 15 2019, In : Journal of Differential Equations. 266, 9, p. 5431-5447 17 p.

Research output: Contribution to journalArticle

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

Computer-assisted Proof
Biharmonic Problem
Biharmonic Equation
Computational Techniques
Error Estimation
2016
1 Citation (Scopus)
Computer-assisted Proof
Numerical Verification
Rounding error
Floating point
Steady-state Solution
3 Citations (Scopus)
Numerical Verification
Functional equation
Nonlinear Equations
Computer-assisted Proof
Iteration
2 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

Invertibility
Hilbert spaces
Enclosures
Partial differential equations
Linear Operator
1 Citation (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

Regular Solution
Poisson equation
A Priori Estimates
Poisson's equation
A Priori Error Estimates
2015
3 Citations (Scopus)
Elliptic Operator
Nonlinear Problem
Eigenvalue
Approximate Solution
Computer program listings
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

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

Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces

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

Research output: Contribution to journalArticle

Hilbert spaces
Set theory
Eigenvalue Problem
Mathematical operators
Hilbert space
2013
7 Citations (Scopus)

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

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

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

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

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

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

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

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

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

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

Numerical Verification
Rayleigh
Three-dimensional
Fluids
Computer-assisted Proof
1 Citation (Scopus)
Numerical Verification
Rayleigh
Elliptic Equations
Heat convection
Bifurcation Point
2008
13 Citations (Scopus)

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

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

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

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., Jan 1 2005, In : Japan Journal of Industrial and Applied Mathematics. 22, 1, p. 111-131 21 p.

Research output: Contribution to journalArticle

Numerical Verification
A Priori Error Estimates
Singularly Perturbed Problem
Nonlinearity
Exponential Fitting
2004
15 Citations (Scopus)

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

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

Research output: Contribution to journalArticle

Numerical Verification
Elliptic Differential Equations
Differential equations
Derivatives
Poisson equation
16 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

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

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

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

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

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., Jan 1 2001, In : Japan Journal of Industrial and Applied Mathematics. 18, 2, p. 587-602 16 p.

Research output: Contribution to journalArticle

Enclosure
Enclosures
Elliptic Problems
Numerical Computation
Eigenvalue Problem
1998
7 Citations (Scopus)

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

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

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

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

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

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

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

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

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