kKyushu Universityl
Watanabe, Yoshitaka
Associate Professor, Doctor of Mathematics
Research Institute for Information Technology
Japanese Version
 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:
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. 629636.
doi:10.1007/s131600160223y

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. 157170.
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. 63636374, 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
Infinitedimensional Newtonlike Iteration,
Applied Mathematics and Computation,
Vol. 276, (March 2016) pp. 239251.
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. 1932.
DOI 10.1007/s1316001401606

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. 975992.
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. 4752.

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. 15431557.

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. 2333.

Shuting Cai, Kaori Nagatou, and Yoshitaka Watanabe:
A Numerical Verification Method for a System of
FitzHughNagumo Type,
Numerical Functional Analysis and Optimization,
Vol. 33, No. 10 (October 2012) pp. 11951220.

Nobito Yamamoto, Mitsuhiro T. Nakao, and Yoshitaka Watanabe:
A Theorem for Numerical Verification on Local Uniqueness of Solutions
to FixedPoint Equations,
Numerical Functional Analysis and Optimization,
Vol. 32, No. 11 (November 2011) pp. 11901204.

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto,
Takaaki Nishida and MyoungNyoun Kim:
Computer Assisted Proofs of Bifurcating Solutions for
Nonlinear Heat Convection Problems,
Journal of Scientific Computing,
Vol. 43, No. 3 (June 2010) pp. 388401.

Yoshitaka Watanabe and Mitsuhiro T. Nakao:
Numerical Verification Method of Solutions
for Elliptic Equations and Its Application
to the RayleighBénard Problem,
Japan Journal of Industrial and Applied Mathematics,
Vol. 26, No. 23 (October 2009) pp. 443463.

Yoshitaka Watanabe:
A Numerical Verification Method for TwoCoupled Elliptic Partial Differential
Equations,
Japan Journal of Industrial and Applied Mathematics,
Vol. 26, No. 23 (October 2009) pp. 233247.

Yoshitaka Watanabe:
A Computerassisted Proof for the Kolmogorov Flows of Incompressible
Viscous Fluid,
Journal of Computational and Applied Mathematics,
Vol.223 (Jan. 2009) pp.953966.

Yoshitaka Watanabe, Michael Plum and Mitsuhiro T. Nakao:
A Computerassisted Instability Proof for the OrrSommerfeld Problem
with Poiseuille Flow,
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
Journal of Applied Mathematics and Mechanics,
Vol.89, No.1, pp.518 (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 3dimensional
RayleighBénard Problems,
Numerische Mathematik,
Vol.111, No.3 (Jan. 2009) pp.389406.

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.114.
Special issue: GAMM  Workshop on Guaranteed Errorbounds 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, Issue14 (2004) pp.311323.
Special Issue: SCAN'2002 International Conference
(Guest Editors: Rene Alt and JeanLuc 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.120.

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.359372.
(Special Issue Proceedings of the Validated Computing 2002 conference,
May 2325, 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.175190.

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.567585.

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 JapanChina Joint Seminar on Numerical Mathematics,
held in Chiba, Japan, August 2428, 1998
(H. Kawarada, M. Nakamura, Z. Shi, eds.),
GAKUTO International Series Mathematical Sciences and Applications, Volume 12,
Gakkotosho, Tokyo, Japan (1999) pp.155162.

Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:
A Numerical Verification Method of Solutions
for the NavierStokes Equations,
Reliable Computing,
Vol.5, No.3 (1999) pp.347357.

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.137150 (Japanese).

Mitsuhiro T. Nakao, Nobito Yamamoto and Yoshitaka Watanabe:
Constructive L^{2} Error Estimates for Finite Element Solutions
of the Stokes Equations,
Reliable Computing,
Vol.4, No.2 (1998) pp.115124.

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.137158.

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.577587.

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 SCAN95, held in Wuppertal,
Germany, September 2629, 1995 (G. Alefeld, A. Frommer, B. Lang,
eds.), Mathematical Research, Volume 90, Akademie Verlag
(1996) pp.258264.

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.13 (1994) pp.401410.

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.165178.
 Address:
 Research Institute for Information Technology, Kyushu University
 Fukuoka 8128581, JAPAN
 email: watanabe
@
cc.
kyushuu.ac.jp