[Kyushu University]

Watanabe, Yoshitaka

Associate Professor, Doctor of Mathematics
Research Institute for Information Technology

Japanese Version

• program code for "Another computer-assisted proof of unimodality of solutions for Proudman-Johnson equation"
• program code for "Inclusion method of optimal constant with quadratic convergence for H10-projection error estimates and its applications"
• For "Computer-assisted proofs toward the critical Reynolds number for the Orr-Sommerfeld Problem"
  • proof of Lemma4.1 (PDF file; 344KB)
  • proof of Lemma4.2 (PDF file; 115KB)
• Program code for "Computer assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem" (Kolmogorov-2021.tar.gz)
• program code for "Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces"
• program code for "A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow"

Member of:

The Japan Society for Industrial and Applied Mathematics(JSIAM)

Mathematical Society of Japan

Research Topics:

Field:

Numerical Methods with Guaranteed accuracy, Computer Assisted Proof, Numerical Computation for Partial Differential Equations

Keywords:

Numerical Verification, Interval Arithmetic, Finite Element Method

List of Recent Publications:

• Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, and Mitsuhiro T. Nakao:
  Inclusion method of optimal constant with quadratic convergence for H10-projection error estimates and its applications,
  Journal of Computational and Applied Mathematics, Vol. 417 (January 2023) 114521.
  https://doi.org/10.1016/j.cam.2022.114521

• Shuting Cai, Yoshitaka Watanabe:
  A computer-assisted method for the diblock copolymer model,
  Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM); Journal of Applied Mathematics and Mechanics, Volume 99, Issue 7 (July 2019) e201800125.
  https://doi.org/10.1002/zamm.201800125

• Yoshitaka Watanabe, Takehiko Kinoshita, and Mitsuhiro T. Nakao:
  An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space,
  Japan Journal of Industrial and Applied Mathematics, Volume 36, Issue 2 (July 2019) pp. 407-420.
  https://doi-org.anywhere.lib.kyushu-u.ac.jp/10.1007/s13160-019-00344-8

• Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao:
  An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces,
  Journal of Differential Equations, vol. 266, Issue 9 (April 2019) pp. 5431-5447.
  https://doi.org/10.1016/j.jde.2018.10.027

• Yoshitaka Watanabe, Mitsuhiro T. Nakao, and Kaori Nagatou:
  On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations,
  JSIAM Letters, vol. 9 (December 2017) pp. 77-80.
  doi://doi.org/10.14495/jsiaml.9.77

• Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao:
  Validated constructive error estimations for biharmonic problems,
  in Scientific Computing, Computer Arithmetic, and Validated Numerics; 17th International Symposium, SCAN 2016, Uppsala, Sweden, September 26-29, 2016. Revised Selected Papers (V. Kreinovich, W. Tucker, eds.), Reliable Computing, vol. 25 (August 2017) pp. 168-177.

• Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, and Mitsuhiro T. Nakao:
  Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains,
  Japan Journal of Industrial and Applied Mathematics, vol. 33, Issue 3 (December 2016) pp. 629-636.
  doi:10.1007/s13160-016-0223-y

• Yoshitaka Watanabe:
  An Efficient Numerical Verification Method for the Kolmogorov Problem of Incompressible Viscous Fluid,
  Journal of Computational and Applied Mathematics, Vol. 302 (August 2016) pp. 157-170.
  doi:10.1016/j.cam.2016.01.055

• Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, and Mitsuhiro T. Nakao:
  Norm Bound Computation for Inverses of Linear Operators in Hilbert Spaces,
  Journal of Differential Equations, Vol. 260, Issue 7 (April 2016) pp. 6363-6374, 2016.
  doi:10.1016/j.jde.2015.12.041

• Yoshitaka Watanabe and Mitsuhiro T. Nakao:
  A Numerical Verification Method for Nonlinear Functional Equations Based on Infinite-dimensional Newton-like Iteration,
  Applied Mathematics and Computation, Vol. 276, (March 2016) pp. 239-251.
  doi:10.1016/j.amc.2015.12.021

• Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, and Nobito Yamamoto:
  Some Considerations of the Invertibility Verifications for Linear Elliptic Operators,
  Japan Journal of Industrial and Applied Mathematics, Vol. 32, No. 1 (March 2015) pp. 19-32.
  DOI 10.1007/s13160-014-0160-6

• Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, and Mitsuhiro T. Nakao:
  Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces,
  SIAM Journal on Numerical Analysis, Vol. 52, No. 2 (May 2014) pp. 975-992.
  http://dx.doi.org/10.1137/120894683

• Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao:
  An Improvement of the Theorem of A Posteriori Estimates for Inverse Elliptic Operators,
  Nonlinear Theory and Its Applications, IEICE, Vol. 5, No. 1 (January 2013) pp. 47-52.
  

• Yoshitaka Watanabe, Takehiko Kinoshita, and Mitsuhiro T. Nakao:
  A Posteriori Estimates of Inverse Operators for Boundary Value Problems in Linear Elliptic Partial Differential Equations,
  Mathematics of Computation, Vol. 82, No. 283 (July 2013) pp. 1543-1557.
  

• Yoshitaka Watanabe:
  A Simple Numerical Verification Method for Differential Equations Based on Infinite Dimensional Sequential Iteration,
  Nonlinear Theory and Its Applications, IEICE, Vol. 4, No. 1 (January 2013) pp. 23-33.
  

• Shuting Cai, Kaori Nagatou, and Yoshitaka Watanabe:
  A Numerical Verification Method for a System of FitzHugh-Nagumo Type,
  Numerical Functional Analysis and Optimization, Vol. 33, No. 10 (October 2012) pp. 1195-1220.
  

• Nobito Yamamoto, Mitsuhiro T. Nakao, and Yoshitaka Watanabe:
  A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations,
  Numerical Functional Analysis and Optimization, Vol. 32, No. 11 (November 2011) pp. 1190-1204.
  

• Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida and Myoung-Nyoun Kim:
  Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems,
  Journal of Scientific Computing, Vol. 43, No. 3 (June 2010) pp. 388-401.
  

• Yoshitaka Watanabe and Mitsuhiro T. Nakao:
  Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh-Bénard Problem,
  Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3 (October 2009) pp. 443-463.
  

• Yoshitaka Watanabe:
  A Numerical Verification Method for Two-Coupled Elliptic Partial Differential Equations,
  Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3 (October 2009) pp. 233-247.
  

• Yoshitaka Watanabe:
  A Computer-assisted Proof for the Kolmogorov Flows of Incompressible Viscous Fluid,
  Journal of Computational and Applied Mathematics, Vol.223 (Jan. 2009) pp.953-966.

• Yoshitaka Watanabe, Michael Plum and Mitsuhiro T. Nakao:
  A Computer-assisted Instability Proof for the Orr-Sommerfeld Problem with Poiseuille Flow,
  Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) Journal of Applied Mathematics and Mechanics, Vol.89, No.1, pp.5-18 (Jan. 2009) / DOI 10.1002/zamm.200700158.

• Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaaki Nishida:
  A Numerical Verification Method of Bifurcating Solutions for 3-dimensional Rayleigh-Bénard Problems,
  Numerische Mathematik, Vol.111, No.3 (Jan. 2009) pp.389-406.

• Mitsuhiro T. Nakao, Kouji Hashimoto and Yoshitaka Watanabe:
  A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems,
  Computing, Vol.75, Number 1 (July 2005) pp.1-14.
  Special issue: GAMM - Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics. Guest Editor: Jurgen Herzberger.

• Mitsuhiro T. Nakao, Yoshitaka Watanabe:
  An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations,
  Numerical Algorithms, Vol.37, Issue1-4 (2004) pp.311-323.
  Special Issue: SCAN'2002 International Conference (Guest Editors: Rene Alt and Jean-Luc Lamotte)

• Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao and Takaaki Nishida:
  A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem,
  Journal of Mathematical Fluid Mechanics, Vol.6, No.1 (2004) pp.1-20.
  

• Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto and Takaaki Nishida:
  Some Computer Assisted Proofs for Solutions of the Heat Convection Problems,
  Reliable Computing, Vol.9, No.5 (2003) pp.359-372.
  (Special Issue Proceedings of the Validated Computing 2002 conference, May 23-25, 2002, Toronto, Canada, Guest Editor: R. Baker Kearfott)

• Kenji Toyonaga, Mitsuhiro T. Nakao and Yoshitaka Watanabe:
  Verified Numerical Computations for Multiple and Nearly Multiple Eigenvalues of Elliptic Operators,
  Journal of Computational and Applied Mathematics, Vol.147, Issue 1 (2002) pp.175-190.

• Mitsuhiro T. Nakao, Yoshitaka Watanabe and Nobito Yamamoto:
  Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data,
  Japan Journal of Industrial and Applied Mathematics, Vol.18, No.2 (2001) pp.567-585.

• Nobito Yamamoto, Mitsuhiro T. Nakao and Yoshitaka Watanabe:
  Validated Computation for a Linear Elliptic Problem with a Parameter,
  Advances in Numerical Mathematics; Proceedings of the Fourth Japan-China Joint Seminar on Numerical Mathematics, held in Chiba, Japan, August 24-28, 1998 (H. Kawarada, M. Nakamura, Z. Shi, eds.), GAKUTO International Series Mathematical Sciences and Applications, Volume 12, Gakkotosho, Tokyo, Japan (1999) pp.155-162.

• Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:
  A Numerical Verification Method of Solutions for the Navier-Stokes Equations,
  Reliable Computing, Vol.5, No.3 (1999) pp.347-357.

• Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:
  Verification Methods of Generalized Eigenvalue Problems and its Applications,
  Transactions of the Japan Society for Industrial and Applied Mathematics , Vol.9, No.3 (1999) pp.137-150 (Japanese).

• Mitsuhiro T. Nakao, Nobito Yamamoto and Yoshitaka Watanabe:
  Constructive L² Error Estimates for Finite Element Solutions of the Stokes Equations,
  Reliable Computing, Vol.4, No.2 (1998) pp.115-124.

• Mitsuhiro T. Nakao, Nobito Yamamoto and Yoshitaka Watanabe:
  A Posteriori and Constructive A Priori Error Bounds for Finite Element Solutions of the Stokes Equations,
  Journal of Computational and Applied Mathematics, Vol.91 (1998) pp.137-158.

• Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:
  Verified Computations of Solutions for Nondifferentiable Elliptic Equations Related to MHD Equilibria,
  Nonlinear Analysis, Theory, Methods & Applications, Vol.28, No.3 (1997) pp.577-587.

• Mitsuhiro T. Nakao, Nobito Yamamoto and Yoshitaka Watanabe:
  Guaranteed Error Bounds for the Finite Element Solutions of the Stokes Problem,
  Scientific Computing and Validated Numerics, Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95, held in Wuppertal, Germany, September 26-29, 1995 (G. Alefeld, A. Frommer, B. Lang, eds.), Mathematical Research, Volume 90, Akademie Verlag (1996) pp.258-264.

• Mitsuhiro T. Nakao and Yoshitaka Watanabe:
  On Computational Proofs of the Existence of Solutions to Nonlinear Parabolic Problems,
  Journal of Computational and Applied Mathematics, Vol.50, No.1-3 (1994) pp.401-410.

• Yoshitaka Watanabe and Mitsuhiro T. Nakao:
  Numerical Verifications of Solutions for Nonlinear Elliptic Equations,
  Japan Journal of Industrial and Applied Mathematics, Vol.10, No.1 (1993) pp.165-178.

Address:

Research Institute for Information Technology, Kyushu University

Fukuoka 812-8581, JAPAN

e-mail: watanabe@cc.kyushu-u.ac.jp