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Jean-Philippe Lessard
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Validated continuation for equilibria of PDEs
S Day, JP Lessard, K Mischaikow
SIAM Journal on Numerical Analysis 45 (4), 1398-1424, 2007
1382007
Rigorous numerics for symmetric connecting orbits: Even homoclinics of the Gray–Scott equation
JB Van Den Berg, JD Mireles-James, JP Lessard, K Mischaikow
SIAM Journal on Mathematical Analysis 43 (4), 1557-1594, 2011
922011
Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
A Hungria, JP Lessard, J Mireles James
Mathematics of Computation 85 (299), 1427-1459, 2016
872016
Rigorous numerics in dynamics
JB van den Berg, JP Lessard
Notices Amer. Math. Soc 62 (9), 1057-1061, 2015
762015
Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
M Gameiro, JP Lessard
Journal of Differential Equations 249 (9), 2237-2268, 2010
762010
Global smooth solution curves using rigorous branch following
J van den Berg, JP Lessard, K Mischaikow
Mathematics of computation 79 (271), 1565-1584, 2010
762010
Rigorous numerics for nonlinear differential equations using Chebyshev series
JP Lessard, C Reinhardt
SIAM Journal on Numerical Analysis 52 (1), 1-22, 2014
712014
Chaotic braided solutions via rigorous numerics: Chaos in the Swift–Hohenberg equation
JB Van Den Berg, JP Lessard
SIAM Journal on Applied Dynamical Systems 7 (3), 988-1031, 2008
702008
Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields
JP Lessard, JD Mireles James, C Reinhardt
Journal of Dynamics and Differential Equations 26 (2), 267-313, 2014
672014
Global bifurcation diagrams of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system
M Breden, JP Lessard, M Vanicat
Acta applicandae mathematicae 128 (1), 113-152, 2013
662013
Stationary coexistence of hexagons and rolls via rigorous computations
JB van den Berg, A Deschênes, JP Lessard, JD Mireles James
SIAM Journal on Applied Dynamical Systems 14 (2), 942-979, 2015
632015
Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
JP Lessard
Journal of Differential Equations 248 (5), 992-1016, 2010
622010
Parameterization of invariant manifolds for periodic orbits I: Efficient numerics via the Floquet normal form
R Castelli, JP Lessard, JD Mireles James
SIAM Journal on Applied Dynamical Systems 14 (1), 132-167, 2015
612015
Computation of maximal local (un) stable manifold patches by the parameterization method
M Breden, JP Lessard, JDM James
Indagationes Mathematicae 27 (1), 340-367, 2016
542016
Automatic differentiation for Fourier series and the radii polynomial approach
JP Lessard, JDM James, J Ransford
Physica D, 2016
532016
A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE
M Gameiro, JP Lessard
SIAM Journal on Applied Dynamical Systems 16 (1), 687-728, 2017
422017
Rigorous numerics in Floquet theory: computing stable and unstable bundles of periodic orbits
R Castelli, JP Lessard
SIAM Journal on Applied Dynamical Systems 12 (1), 204-245, 2013
422013
Computational fixed-point theory for differential delay equations with multiple time lags
G Kiss, JP Lessard
Journal of Differential Equations 252 (4), 3093-3115, 2012
402012
Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation
M Gameiro, JP Lessard
Numerische Mathematik 117 (4), 753-778, 2011
402011
Validated continuation over large parameter ranges for equilibria of PDEs
M Gameiro, JP Lessard, K Mischaikow
Mathematics and computers in simulation 79 (4), 1368-1382, 2008
372008
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