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OpenAlex Citation Counts

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OpenAlex is a bibliographic catalogue of scientific papers, authors and institutions accessible in open access mode, named after the Library of Alexandria. It's citation coverage is excellent and I hope you will find utility in this listing of citing articles!

If you click the article title, you'll navigate to the article, as listed in CrossRef. If you click the Open Access links, you'll navigate to the "best Open Access location". Clicking the citation count will open this listing for that article. Lastly at the bottom of the page, you'll find basic pagination options.

Requested Article:

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations
Jordi-Lluís Figueras, Marcio Gameiro, J. Lessard, et al.
SIAM Journal on Applied Dynamical Systems (2017) Vol. 16, Iss. 2, pp. 1070-1088
Open Access | Times Cited: 25

Showing 25 citing articles:

Computer-assisted proofs in PDE: a survey
Javier Gómez-Serrano
SeMA Journal (2019) Vol. 76, Iss. 3, pp. 459-484
Open Access | Times Cited: 56
Smooth imploding solutions for 3D compressible fluids
Tristan Buckmaster, Gonzalo Cao Labora, Javier Gómez-Serrano
Forum of Mathematics Pi (2025) Vol. 13
Open Access
Highest cusped waves for the fractional KdV equations
Joel Dahné
Journal of Differential Equations (2024) Vol. 401, pp. 550-670
Open Access | Times Cited: 3
Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation
Roberto Castelli, Marcio Gameiro, J. Lessard
Archive for Rational Mechanics and Analysis (2017) Vol. 228, Iss. 1, pp. 129-157
Open Access | Times Cited: 33
A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
Daniel Wilczak, Piotr Zgliczyński
Journal of Differential Equations (2020) Vol. 269, Iss. 10, pp. 8509-8548
Open Access | Times Cited: 30
Parameterization method for unstable manifolds of delay differential equations
C. M. Groothedde, J. D. Mireles James
Journal of Computational Dynamics (2017) Vol. 4, Iss. 1&2, pp. 21-70
Open Access | Times Cited: 25
An A Posteriori KAM Theorem for Whiskered Tori in Hamiltonian Partial Differential Equations with Applications to some Ill-Posed Equations
Rafael de la Llave, Yannick Sire
Archive for Rational Mechanics and Analysis (2018) Vol. 231, Iss. 2, pp. 971-1044
Closed Access | Times Cited: 25
Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds
William D. Kalies, Shane Kepley, J. D. Mireles James
SIAM Journal on Applied Dynamical Systems (2018) Vol. 17, Iss. 1, pp. 157-202
Open Access | Times Cited: 23
Fourier–Taylor parameterization of unstable manifolds for parabolic partial differential equations: Formalism, implementation and rigorous validation
Christian Reinhardt, J. D. Mireles James
Indagationes Mathematicae (2018) Vol. 30, Iss. 1, pp. 39-80
Open Access | Times Cited: 22
A General Method for Computer-Assisted Proofs of Periodic Solutions in Delay Differential Problems
Jan Bouwe van den Berg, C. M. Groothedde, Jean‐Philippe Lessard
Journal of Dynamics and Differential Equations (2020) Vol. 34, Iss. 2, pp. 853-896
Closed Access | Times Cited: 20
Computer-assisted proofs for radially symmetric solutions of PDEs
István Balázs, Jan Bouwe van den Berg, J.-Y. Courtois, et al.
Journal of Computational Dynamics (2018) Vol. 5, Iss. 1&2, pp. 61-80
Open Access | Times Cited: 15
An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
Journal of Differential Equations (2018) Vol. 266, Iss. 9, pp. 5431-5447
Open Access | Times Cited: 7
Computing Invariant Sets of Random Differential Equations Using Polynomial Chaos
Maxime Breden, Christian Kuehn
SIAM Journal on Applied Dynamical Systems (2020) Vol. 19, Iss. 1, pp. 577-618
Open Access | Times Cited: 7
Constructive error estimates for full discrete approximation of periodic solution for heat equation
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
Journal of Computational and Applied Mathematics (2019) Vol. 368, pp. 112510-112510
Open Access | Times Cited: 6
Validated forward integration scheme for parabolic PDEs via Chebyshev series
Jacek Cyranka, Jean‐Philippe Lessard
Communications in Nonlinear Science and Numerical Simulation (2022) Vol. 109, pp. 106304-106304
Open Access | Times Cited: 4
Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
Journal of Differential Equations (2022) Vol. 338, pp. 76-127
Open Access | Times Cited: 4
Smooth self-similar imploding profiles to 3D compressible Euler
Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano
Quarterly of Applied Mathematics (2023) Vol. 81, Iss. 3, pp. 517-532
Open Access | Times Cited: 2
Rigorous numerical computations for 1D advection equations with variable coefficients
Akitoshi Takayasu, Suro Yoon, Yasunori Endo
Japan Journal of Industrial and Applied Mathematics (2019) Vol. 36, Iss. 2, pp. 357-384
Closed Access | Times Cited: 3
Numerical verification methods for a system of elliptic PDEs, and their software library
Kouta Sekine, Mitsuhiro T. Nakao, Shin’ichi Oishi
Nonlinear Theory and Its Applications IEICE (2020) Vol. 12, Iss. 1, pp. 41-74
Open Access | Times Cited: 1
Rigorous FEM for One-Dimensional Burgers Equation
Piotr Kalita, Piotr Zgliczyński
SIAM Journal on Applied Dynamical Systems (2021) Vol. 20, Iss. 2, pp. 853-907
Closed Access | Times Cited: 1
Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces
Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
Journal of Scientific Computing (2023) Vol. 94, Iss. 2
Open Access
On exponential dichotomy and frameworks for rigorous computation for differential equations
Guilherme Kenji Nakassima
(2023)
Open Access
Computing invariant sets of random differential equations using polynomial chaos
Maxime Breden, Christian Kuehn
arXiv (Cornell University) (2018)
Closed Access
Computer-Assisted Proofs for Dynamical Systems
Mitsuhiro T. Nakao, Michael Plum, Yoshitaka Watanabe
Springer series in computational mathematics (2019), pp. 415-421
Closed Access
Rigorous FEM for 1D Burgers equation
Piotr Kalita, Piotr Zgliczyński
arXiv (Cornell University) (2020)
Open Access
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