- K. Matsue and A. Takayasu:
*"Numerical validation of blow-up solutions with quasi-homogeneous compactifications"*, submitted 2017. (arXiv:1707.05936)

Code associated to the paper is available here.

- A. Takayasu, M. Mizuguchi, T. Kubo, and S. Oishi:

*"Accurate method of verified computing for solutions of semilinear heat equations"*, Reliable computing, Vol. 25, pp. 74-99, July 2017. (PDF, arXiv:1611.10243)

Code associated to the paper is available here. - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:

*"A method of verified computations for solutions to semilinear parabolic equations using semigroup theory"*, SIAM J. Numer. Anal., Vol. 55, No. 2, pp. 980-1001, Apr. 2017. (DOI:10.1137/141001664, PDF) - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:

*"Numerical verification for existence of a global-in-time solution to semilinear parabolic equations"*, J. Comput. Appl. Math., Vol. 315, pp. 1-16, May 2017 (available online Nov. 2016). (DOI:10.1016/j.cam.2016.10.024, PDF) - A. Takayasu, K. Matsue, T. Sasaki, K. Tanaka, M. Mizuguchi, and S. Oishi:

*"Numerical validation of blow-up solutions of ordinary differential equations"*, J. Comput. Appl. Math., Vol. 314, pp. 10-29, Apr. 2017 (available online Oct. 2016). (DOI:10.1016/j.cam.2016.10.013, arXiv:1606.03039) - M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:

*"On the embedding constant of the Sobolev type inequality for fractional derivatives"*, NOLTA, IEICE, Vol. 7, No. 3, pp. 386-394, Jul. 2016. (DOI:10.1587/nolta.7.386, PDF) - N. Hoffman, K. Ichihara, M. Kashiwagi, H. Masai, S. Oishi, and A. Takayasu:

*"Verified computations for hyperbolic 3-manifolds"*, Exp. Math., Vol. 25, Issue 1, pp. 66-78, 2016 (available online Oct. 2015). (DOI:10.1080/10586458.2015.1029599, arXiv:1310.3410)

Code associated to the paper is available here. - K. Tanaka, A. Takayasu, X. Liu, S. Oishi:
*"Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation"*, Jpn. J. Ind. Appl. Math., Vol. 31, Issue 3, pp. 665-679, Nov. 2014. (DOI:10.1007/s13160-014-0156-2) - A. Takayasu, X. Liu, S. Oishi:

*"Remarks on computable a priori error estimates for finite element solutions of elliptic problems"*, NOLTA, IEICE, Vol. 5, No. 1, pp. 53-63, Jan. 2014. (DOI:10.1587/nolta.5.53) - K. Sekine, A. Takayasu, S. Oishi:

*"An algorithm of identifying parameters satisfying a sufficient condition of Plum's Newton-Kantorovich like existence theorem for nonlinear operator equations"*, NOLTA, IEICE, Vol. 5, No. 1, pp. 64-79, Jan. 2014. (DOI:10.1587/nolta.5.64) - A. Takayasu, X. Liu, S. Oishi:

*"Verified computations to semilinear elliptic boundary value problems on arbitrary polygonal domains"*, NOLTA, IEICE, Vol. 4, No. 1, pp. 34-61, Jan. 2013. (DOI:10.1587/nolta.4.34) - A. Takayasu, S. Oishi:

*"A method of computer assisted proof for nonlinear two-point boundary value problems using higher order finite elements"*, NOLTA, IEICE, Vol. 2, No. 1, pp. 74-89, Jan. 2011. (DOI:10.1587/nolta.2.74) - A. Takayasu, S. Oishi, T. Kubo:

*"Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations"*, NOLTA, IEICE, Vol. 1, No. 1, pp. 105-118, Oct. 2010. (DOI:10.1587/nolta.1.105)

- A. Takayasu, M. Mizuguchi, T. Kubo, S. Oishi:

*"Verified Computations for Solutions to Semilinear Parabolic Equations Using the Evolution Operator"*, in*Mathematical Aspects of Computer and Information Sciences*,

Volume 9582 of the series Lecture Notes in Computer Science, pp. 218-223, Springer International Publishing, Switzerland, 2016. - A. Takayasu, S. Oishi:

*"A verified continuation algorithm for solution curve of nonlinear elliptic equations"*,

Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications (NOLTA 2013), US, 2013, pp.441-444. - A. Takayasu, S. Oishi:

*"A computer-assisted proof method of the invertibility to elliptic operators"*,

Proceedings of 2012 International Symposium on Nonlinear Theory and its Applications (NOLTA 2012), Spain, 2012, pp.816-819. - A. Takayasu, X. Liu, S. Oishi:

*"Computer assisted proofs for solutions to nonlinear elliptic partial differential equations on arbitrary polygonal domain"*,

Proceedings of 2011 International Symposium on Nonlinear Theory and its Applications (NOLTA 2011), Japan, 2011, pp.90-93. - A. Takayasu, S. Oishi, T. Kubo:

*"Computer assisted proofs of solutions to Nonlinear elliptic partial differential equations"*,

Proceedings of 2010 International Symposium on Nonlinear Theory and its Applications (NOLTA 2010), Poland, 2010, pp.135-138. - A. Takayasu, S. Oishi, T. Kubo:

*"A priori inverse operator estimation for guaranteed error estimate"*,

Proceedings of 4th Workshop on Reliable Engineering Computing (REC2010) "Robust Design - Coping with Hazards, Risk and Uncertainty", Singapore, 2010, pp.649-664. - A. Takayasu, S. Oishi, T. Kubo:

*"Guaranteed error estimate for solutions to two-point boundary value problem"*,

Proceedings of 2009 International Symposium on Nonlinear Theory and its Applications (NOLTA 2009), Japan, 2009, pp.214-217. - A. Takayasu, S. Oishi, T. Kubo:

*"Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM"*,

Proceedings of ASIA SIMULATION CONFERENCE 2009 (JSST 2009), Japan, 2009, Paper ID: 163 (8 pages). - A. Takayasu, S. Oishi, T. Kubo:

*"Numerical verification for solutions to nonlinear two-point boundary value problems with finite element method"*,

Proceedings of the 24th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2009), Korea, 2009, pp.165-168.

- A. Takayasu, X. Liu, S. Oishi:

*"A residual bound evaluation of operator equations with Raviart-Thomas finite element"*,

RIMS Kokyuroku,**1791**(2012), pp.206-215. - A. Takayasu, S. Oishi:

*"A refinement technique to residual evaluation of Computer assisted proofs for Semilinear elliptic boundary value problems"*,

RIMS Kokyuroku,**1733**(2011), pp.118-126. - A. Takayasu, S. Oishi, T. Kubo:

*"Numerical Existence Proofs and Guaranteed Error Bounds for Solutions to Two-Point Boundary Value Problems"*,

RIMS Kokyuroku,**1719**(2010), pp.48-60.

- Akitoshi Takayasu:

*"Rigorous numerical computations for 1-dimensional advection equations with variable coefficients"*,

Workshop for young scholars Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods -, Kyoto, Japan (2017/8/21). - Akitoshi Takayasu, Kaname Matsue:

*"Numerical validation of blow-up solutions via quasi-parabolic compactifications"*,

The International Workshop on Numerical Verification and its Applications 2017 (INVA 2017), Okinawa, Japan (2017/3/15). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Computable norm bounds of the evolution operator using spectral properties"*,

The 35th JSST Annual Conference International Conference on Simulation Technology (JSST2016), Kyoto, Japan (2016/10/28). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"On verification methods for parabolic partial differential equations using the evolution operator"*,

the 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics (SCAN 2016), Uppsala, Sweden (2016/9/28). - Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi:

*"Verified numerical computations for blow-up solutions of ODEs"*,

the 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics (SCAN 2016), Uppsala, Sweden (2016/9/26). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Computable estimates of the evolution operator based on the operator theory"*,

Czech-Japanese-Polish Seminar in Applied Mathematics 2016 (CJPS 2016), Krakow, Polland (2016/9/8). - Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"Verification algorithm for enclosing a mild solution of semilinear heat equations"*,

The fifth Asian conference on Nonlinear Analysis and Optimization (NAO-Asia 2016), Niigata, Japan (2016/8/2). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Concatenation scheme for verified inclusion of solutions to semilinear heat equations"*,

The fifth Asian conference on Nonlinear Analysis and Optimization (NAO-Asia 2016), Niigata, Japan (2016/8/2). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Verified Computations for Solutions to Nonlinear Heat Equations Based on Fractional Powers of a Positive Operator and the Evolution Operator"*,

5th European Seminar on Computing (ESCO 2016), Pilsen, Czech Republic (2016/6/9). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Verified computations for solutions to semilinear parabolic equations using the evolution operator"*,

Sixth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS2015), Berlin, Germany (2015/11/12). - Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi:

*"Numerical existence theorem for solutions of semilinear parabolic equations using the evolution operator"*,

The 34th JSST Annual Conference International Conference on Simulation Technology (JSST2015), Toyama, Japan (2015/10/12). - Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"Verified computations for solutions of semilinear heat equations using an analytic semigroup generated by a self-adjoint operator"*,

The 34th JSST Annual Conference International Conference on Simulation Technology (JSST2015), Toyama, Japan (2015/10/12). - Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"Numerical verification of solutions for the Fujita type parabolic equations"*,

The 14th Asia Simulation Conference & The 33rd JSST Annual Conference: International Conference on Simulation Technology (AsiaSim & JSST 2014), Kitakyushu, Japan (2014/10/30). - Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi:

*"A numerical verification method using $H^1_sigma$-norm for an elliptic system of FitzHugh-Nagumo type"*,

The 14th Asia Simulation Conference & The 33rd JSST Annual Conference: International Conference on Simulation Technology (AsiaSim & JSST 2014), Kitakyushu, Japan (2014/10/30). - Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"A sharper error estimate of verified computations for nonlinear heat equations"*,

16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN2014), Würzburg, Germany (2014/9/23). - Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"A method of verified computations for nonlinear parabolic equations"*,

16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN2014), Würzburg, Germany (2014/9/23). - Akitoshi Takayasu:

*"An approach for verified computations of semilinear parabolic equations using the semigroup theory"*,

ICIAM 2014 Scientific Workshop, Ohio, US (2014/5/15). With M. Mizuguchi, T. Kubo, and S. Oishi. - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Verified numerical classification of non-trivial solutions to elliptic equations"*,

The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014), Kyoto, Japan (2014/3/20). - Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"A method of verified computations for nonlinear homogeneous heat equations, Part I: Enclosure of semidiscrete approximate solution for space variable"*,

The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014), Tokyo, Japan (2014/3/16). - Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi:

*"A method of verified computations for nonlinear homogeneous heat equations, Part II: Semigroup approach to construct an exact solution for time variable"*,

The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014), Tokyo, Japan (2014/3/16). - Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi:

*"Computer assisted proof for existence of solutions to a system of elliptic partial differential equations"*,

The International Workshop on Numerical Verification and its Applications 2014 (INVA 2014), Tokyo, Japan (2014/3/15). - Shin'ichi Oishi (substitute speaker: Akitoshi Takayasu):

*"Numerical Verification of Hyperbolicity for 3-Manifolds"*,

The Second International Conference on Engineering and Computational Mathematics(ECM2013), The Hong Kong Polytechnic University, Hong Kong (2013/12/18). - Makoto Mizuguchi, Takayuki Kubo, Akitoshi Takayasu, Shin'ichi Oishi:

*"A priori error estimate of inhomogeneous heat equations using rational approximation of semigroups"*,

International Conference on Simulation Technology (JSST 2013), Meiji University, Tokyo, Japan (2013/9/13). - Kazuaki Tanaka, Makoto Mizuguchi, Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi:

*"Estimation of an embedding constant on Lipschitz domains using extension operators"*,

International Conference on Simulation Technology (JSST 2013), Meiji University, Tokyo, Japan (2013/9/13). - Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi:

*"A verified computation of steady-state solutions to Reaction-Diffusion equations"*,

International Conference on Simulation Technology (JSST 2013), Meiji University, Tokyo, Japan (2013/9/13). - Akitoshi Takayasu, Shin'ichi Oishi:

*"A verified continuation algorithm for solution curve of nonlinear elliptic equations"*,

2013 International Symposium on Nonlinear Theory and its Applications (NOLTA 2013), Santa Fe, US (2013/9/11). - Kazuaki Tanaka, Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Verified norm estimation for the inverse of linear elliptic operators and its application"*,

The 9th East Asia SIAM Conference & The 2nd Conference on Industrial and Applied Mathematics (EASIAM 2013-CIAM 2013), West Java, Indonesia (2013/6/19). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Verified computations for elliptic boundary value problems on arbitrary polygonal domains"*,

The Tenth Asian Symposium on Computer Mathematics (ASCM 2012), Beijing, China (2012/10/28). - Akitoshi Takayasu, Shin'ichi Oishi:

*"A computer-assisted proof method of the invertibility to elliptic operators"*,

2012 International Symposium on Nonlinear Theory and its Applications (NOLTA 2012), Palma Majorca, Spain (2012/10/26). - Kouta Sekine, Akitoshi Takayasu, Shin'ichi Oishi:

*"A numerical verification method for solutions to systems of elliptic partial differential equations"*,

15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN'2012), Novosibirsk, Russia (2012/9/24). - Akitoshi Takayasu, Shin'ichi Oishi:

*"Computer-assisted error analysis for second-order elliptic equations in divergence form"*,

15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN'2012), Novosibirsk, Russia (2012/9/24). - Akitoshi Takayasu, Shin'ichi Oishi:

*"Computer-assisted existence proof of solutions to elliptic equations in divergence form"*,

The 8th East Asia SIAM Conference (EASIAM 2012), Taipei, Taiwan (2012/6/27). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Verified numerical computations for solutions to semilinear elliptic boundary value problems on arbitrary polygonal domains"*,

Fifth Conference on Numerical Analysis and Applications (NAA'12), Lozenetz, Bulgaria (2012/6/18). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Computer Assisted Proofs for Solutions to Nonlinear Elliptic Partial Diﬀerential Equations on Arbitrary Polygonal Domain"*,

2011 International Symposium on Nonlinear Theory and its Applications (NOLTA 2011), Hyogo, Japan (2011/9/5). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"A Method of computer assisted proof for Semilinear elliptic equations on Arbitrary polygonal domain"*,

The 7th International Congress on Industrial and Applied Mathematics (ICIAM 2011), Vancouver, Canada (2011/7/20). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"Numerical verification for solution existence of elliptic PDE on arbitrary polygonal domain"*,

The 7th East Asia SIAM Conference & RIMS Workshop on Methods in Industrial and Applied Mathematics (EASIAM 2011), Kitakyushu, Japan (2011/6/29). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi:

*"A computer assisted proof method for semilinear elliptic equations on arbitrary polygonal domain"*,

Workshop on Analytic and Computational Techniques in Spectral Theory and Related Topics (EPSRC Gregynog Workshop 2011), Gregynog Hall, UK (2011/6/21). - Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi, Takayuki Kubo:

*"Numerical existence proofs and Accurate error bounds of solutions to Semilinear elliptic equations with higher order finite elements"*,

14th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2010), ENS de Lyon, France (2010/9/30). - Shin'ichi Oishi, Akitoshi Takayasu, Takayuki Kubo:

*"Numerical Verification of Existence for Solutions to Dirichlet Boundary Value Problems of Semilinear Elliptic Equations"*,

14th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2010), ENS de Lyon, France (2010/9/30). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Computer assisted proofs of solutions to Nonlinear elliptic partial differential equations"*,

2010 International Symposium on Nonlinear Theory and its Applications (NOLTA 2010), Krakow, Poland (2010/8/6). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Numerical Existence Theorem for Semilinear Elliptic Boundary Value Problems II"*,

2010 International Workshop on Numerical Verification and its Applications (INVA2010), Hachijo-jima, Japan (2010/3/11). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"A priori inverse operator estimation for guaranteed error estimate"*,

4th Workshop on Reliable Engineering Computing (REC2010) "Robust Design - Coping with Hazards, Risk and Uncertainty", Hotel Furama Riverfront, Singapore (2010/3/5). - Shin'ichi Oishi, Akitoshi Takayasu, Takayuki Kubo:

*"Numerical Verification Method for Nonlinear Differential Equations"*,

The Joint Conference of ASCM2009 and MACIS2009, JAL Resort Sea Hawk Hotel, Fukuoka, Japan (2009/12/15). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Guaranteed error estimate for solutions to two-point boundary value problem"*,

2009 International Symposium on Nonlinear Theory and its Applications (NOLTA 2009), Hokkaido, Japan (2009/10/19). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM"*,

ASIA SIMULATION CONFERENCE 2009 (JSST 2009), Ritsumeikan University, Shiga, Japan (2009/10/8). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Numerical verification for solutions to nonlinear two-point boundary value problems with finite element method"*,

The 24th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2009), Jeju Island, Korea (2009/7/8). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Guaranteed error estimate for solutions to linear two-point boundary value problems"*,

The 2nd International Conference on Mathematical Modelling and Computation and The 5th East Asia SIAM Conference (EASIAM), Bandar Seri Begawan, Brunei Darussalam (2009/6/8). - Akitoshi Takayasu, Shin'ichi Oishi, Takayuki Kubo:

*"Guaranteed error estimate for solutions to nonlinear two-point boundary value problem"*,

2009 International Workshop on Numerical Verification and its Applications (INVA2009), Okinawa, Japan (2009/3/26).

- JSIAM Annual Meeting 2017 Best Poster Award, Sep. 2017.
- JSST 2016 Outstanding Presentation Award, Oct. 2016.
- JSIAM Award for an Excellent Talk by a Young Scientist, Jun. 2016.
- WASEDA e-Teaching Award, Apr. 2016.
- Young Researcher's Award, Japan Society for Simulation Technology (JSST), Oct. 2011.
- EASIAM 2011 Student Paper Competition 3rd Prize, Jun. 2011.

Studies on verified computations for solutions to elliptic boundary value problems (PDF)

Verified Numerical Computations for Boundary Value Problems of Differential Equations

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