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Yoshitaka Watanabe Last modified date:2018.04.24



Graduate School
Undergraduate School


E-Mail
Homepage
http://ri2t.kyushu-u.ac.jp/~watanabe/
Watanabe Yoshitaka's home page .
Academic Degree
Doctor of Mathematics
Field of Specialization
Numerical Analysis
Research
Research Interests
  • a posteriori estimate for solutions of nonlinear PDE
    keyword : PDF, Numerical verification, FEM
    2002.04.
Academic Activities
Papers
1. Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, 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, 10.1007/s13160-016-0223-y, 33, 3, 629-636, 2016.12.
2. Yoshitaka Watanabe, An Efficient Numerical Verification Method for the Kolmogorov Problem of Incompressible Viscous Fluid, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2016.01.055, 302, 157-170, 2016.09.
3. Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Norm Bound Computation for Inverses of Linear Operators in Hilbert Spaces, Journal of Differential Equations , 10.1016/j.jde.2015.12.041, 260, 7, 6363-6374, 2016.04.
4. Yoshitaka Watanabe, Mitsuhiro T. Nakao, A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration, Applied Mathematics and Computation, doi:10.1016/j.amc.2015.12.021, 276, 239-251, 2016.03, 無限次元Hilbert空間の非線形関数方程式に対し、弱形式に基づく残差引き戻しと無限次元Newton法を組み合わせた堅牢な解の存在検証理論を提案し、非線形偏微分方程式を含む具体的な問題に対する計算機援用証明により、その有効性を明らかにしました。.
5. Shuting Cai, Yoshitaka Watanabe, A Computer-assisted Method for Excluding Eigenvalues of an Elliptic Operator Linearized at a Solution of a Nonlinear Problem, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-015-0167-7, 32, 1, 263-294, 2015.03.
6. Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, Nobito Yamamoto, Some Considerations of the Invertibility Verifications for Linear Elliptic Operators, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-014-0160-6 , 32, 1, 19-32, 2015.03.
7. Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces, SIAM Journal on Numerical Analysis, 10.1137/120894683, 52, 2, 975-992, 2014.05, 無限次元Hilbert空間における複素数固有値問題の固有値の数学的に厳密な非存在範囲を与える一般定理と、具体的な非存在領域を求めるための精度保証付き数値計算アルゴリズムを提案するとともに、丸め誤差の影響を考慮した具体的な数値例を確認可能なプログラムコードとともに与えた。.
8. Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, A Posteriori Estimates of Inverse Operators for Boundary Value Problems in Linear Elliptic Partial Differential Equations, Mathematics of Computation, 82, 283, 1543-1557, 2013.07.
9. Nobito Yamamoto, Mitsuhiro T. Nakao, Yoshitaka Watanabe, A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations, Numerical Functional Analysis and Optimization, 32, 11, 1190-1204, 2011.11, Nobito Yamamoto, Mitsuhiro T. Nakao, and Yoshitaka Watanabe:.
10. Mitsuhiro T. Nakao, and Yoshitaka Watanabe, Numerical Verification Methods for Solutions of Semilinear Elliptic Boundary Value Problems, Nonlinear Theory and Its Applications, 2, 1, 2-31, 2011.01.
11. 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, 26, 2-3, 443-463, 2009.10.
12. Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao , A computer-assisted instability proof for the Orr-Sommerfeld problemwith Poiseuille flow, Journal of Applied Mathematics and Mechanics (ZAMM), Vol.89, No.1, 5-18, 2009.01.
13. Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaaki Nishida, A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Be\'nard problems, Numerische Mathematik, Vol.111, No.3, pp.389-406, 2009.01.
Presentations
1. Yoshitaka Watanabe, A higher order error estimation of the Poisson equation and its applications , International Workshop on Numerical Methods for Partial Differential Equations , 2018.03.
2. Yoshitaka Watanabe, Some computer-assisted proofs for the Navier-Stokes equations, Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics (17w5141), 2017.05.
3. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, An alternative approach of invertibility verifications for linear operators in Hilbert spaces, The International Workshop on Numerical Verification and its Applications 2017 (INVA 2017), 2017.03.
4. Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, Validated constructive error estimatations for bi-harmonic problems, 17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016), 2016.09.
5. Yoshitaka Watanabe, A nonlinear PDE verification -- Fukuoka, Karlsruhe, Nonlinear PDE Days, 2015.07.
6. Yoshitaka Watanabe, Computer-assisted stability and instability proofs for the Orr-Sommerfeld problem, Institutskolloquien, Institut für Analysis, Karlsruher Institut für Technologie, 2014.09.
7. Yoshitaka Watanabe, A comparison of computer-assisted proofs for the Kolmogorov problem, International Workshop on Numerical Verification and its Applications 2014 (INVA2014), 2014.03.
Awards
  • It is selected in the journal JJIAM.
Educational
Other Educational Activities
  • 2012.11.
  • 2008.03.
  • 2007.03.
  • 2006.03.
  • 2005.03.
  • 2004.03.