Publications

PREPRINTS

[41] M. Breden and J.-P. Lessard. Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs, Submitted, 2017. (pdf) The codes associated to this work can be found here.

[40] I. Balazs, J.B. van den Berg, J. Courtois, J. Dudas, J.-P. Lessard, A. Vörös- Kiss, JF Williams and X.Y. Yin. Computer-assisted proofs for radially symmetric solutions of PDEs, Submitted, 2017. (pdf)

PUBLICATIONS

[39] J.-P. Lessard. Continuation of solutions and studying delay differential equations via rigorous numerics. To appear in Proceedings of Symposia in Applied Mathematics, 2018. (pdf) The codes associated to this work can be found here.

[38] J.B. van den Berg, M. Breden, J.-P. Lessard and M. Murray. Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof, To appear in Journal of Differential Equations, 2017. (pdf)

[37] J.-P. Lessard, E. Sander and T. Wanner. Rigorous continuation of bifurcation points in the diblock copolymer equation, To appear in Journal of Computational Dynamics, 2017. (pdf) The codes associated to this work can be found here.

[36] R. Castelli, J.-P. Lessard and J.D. Mireles James. Parameterization of invariant manifolds for periodic orbits (II): a-posteriori analysis and computer assisted error bounds, To appear in Journal of Dynamics and Differential Equations, 2017. (pdf)

[35] R. Castelli, M. Gameiro and J.-P. Lessard. Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation. To appear in Archive for Rational Mechanics and Analysis, 2017. (pdf) The codes associated to this work can be found here.

[34] J. Jaquette, J.-P. Lessard and K. Mischaikow. Stability and uniqueness of slowly oscillating periodic solutions to Wright’s equation, Journal of Differential Equations, 263(11): 7263-7286, 2017. (pdf) The codes associated to this work can be found here.

[33] G. Kiss and J.-P. Lessard. Rapidly and slowly oscillating periodic oscillations of a delayed van der Pol oscillator. Journal of Dynamics and Differential Equations, 29(4): 1233-1257, 2017. (pdf) The codes associated to this work can be found here.

[32] J.-P. Lessard and J.D. Mireles James. Computer assisted Fourier analysis in sequence spaces of varying regularity. SIAM Journal on Mathematical Analysis, 49(1), 530–561, 2017. (pdf) The codes associated to this work can be found here.

[31] M. Gameiro and J.-P. Lessard. A posteriori verification of invariant objects of evolution equations: periodic orbits in the Kuramoto-Sivashinsky PDE. SIAM Journal on Applied Dynamical Systems, 16(1): 687-728, 2017. (pdf) The codes associated to this work can be found here.

[30] J.-L. Figueras, M. Gameiro, J.-P. Lessard and R. de la Llave. A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. To appear in SIAM Journal on Applied Dynamical Systems, 2017. (pdf)

[29] J.-P. Lessard. Rigorous verification of saddle-node bifurcations in ODEs. Indagationes Mathematicae, 27(4): 1013-1026, 2016. (pdf) The codes associated to this work can be found here.

[28] J.-P. Lessard, J.D. Mireles James and J. Ransford. Automatic differentiation for Fourier series and the radii polynomial approach, Physica D, 334: 174-186, 2016. (pdf) The codes associated to this work can be found here.

[27] M. Gameiro, J.-P. Lessard and A. Pugliese. Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions, Foundations of Computational Mathematics, 16(2): 531-575, 2016. (pdf) The codes associated to this work can be found here.

[26] M. Breden, J.-P. Lessard and J.D. Mireles James. Computation of maximal local (un)stable manifold patches by the parameterization method. Indagationes Mathematicae, 27(1): 340-367, 2016. (pdf) The codes associated to this work can be found here.

[25] A. Hungria, J.-P. Lessard and J.D. Mireles James. Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach, Mathematics of Computation, 85 (299): 1427–1459, 2016. (pdf)

[24] M. Gameiro, J.-P. Lessard and Y. Ricaud. Rigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev series. Journal of Computational and Applied Mathematics, 292: 654-673, 2016. (pdf)

[23] J.B. van den Berg and J.-P. Lessard. Rigorous numerics in dynamics. Notices of the American Mathematical Society, 62(9): 1057-1061, 2015. (pdf)

[22] R. Castelli, J.-P. Lessard and J.D. Mireles James. Analytic enclosure of the fundamental matrix solution. Applications of Mathematics, 60(6): 617-636, 2015. (pdf)

[21] J.B. van den Berg, A. Deschênes, J.-P. Lessard and J.D. Mireles James. Stationary coexistence of hexagons and rolls via rigorous computations. SIAM Journal on Applied Dynamical Systems, 14(2): 942-979, 2015. (pdf) The codes associated to this work can be found here.

[20] L. d’Ambrosio, J.-P. Lessard and A. Pugliese. Blow-up profile for solutions of a fourth order nonlinear equation, Nonlinear Analysis: Theory, Methods and Applications, 121: 280-335, 2015. (pdf) The codes associated to this work can be found here.

[19] M. Breden, L. Desvillettes and J.-P. Lessard. Rigorous numerics for nonlinear operators with tridiagonal dominant linear parts, Discrete and Continuous Dynamical Systems: Series A, 35(10): 4765-4789, 2015. (pdf) The codes associated to this work can be found here.

[18] R. Castelli, J.-P. Lessard and J.D. Mireles James. Parameterization of invariant manifolds for periodic orbits (I): efficient numerics via the Floquet normal form, SIAM Journal on Applied Dynamical Systems, 14(1): 132-167, 2015. (pdf) The codes associated to this work can be found here.

[17] A. Correc and J.-P. Lessard. Coexistence of nontrivial solutions of the one-dimensional Ginzburg-Landau equation: a computer-assisted proof, European Journal of Applied Mathematics, 26(1): 33-60, 2015. (pdf) The codes associated to this work can be found here.

[16] J.-P. Lessard, J.D. Mireles James and C. Reinhardt. Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields. Journal of Dynamics and Differential Equations, 26(2): 267-313, 2014. (pdf)

[15] J.-P. Lessard and C. Reinhardt. Rigorous numerics for nonlinear differential equations using Chebyshev series. SIAM Journal on Numerical Analysis, 52(1): 1-22, 2014. (pdf) The codes associated to this work can be found here.

[14] M. Breden, J.-P. Lessard and M. Vanicat. Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system. Acta Applicandae Mathematicae, 128(1): 113-152, 2013. (pdf)

[13] R. Castelli and J.-P. Lessard. A method to rigorously enclose eigenpairs of complex interval matrices. Applications of Mathematics 2013, Acad. Sci. Czech Repub. Inst. Math., Prague 2013. (pdf)

[12] M. Gameiro and J.-P. Lessard. Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates. SIAM Journal on Numerical Analysis, 51(4): 2063-2087, 2013. (pdf)

[11] R. Castelli and J.-P. Lessard. Rigorous numerics in Floquet theory: computing stable and unstable bundles of periodic orbits. SIAM Journal on Applied Dynamical Systems, 12(1): 204–245, 2013. (pdf) The codes associated to this work can be found here.

[10] G. Kiss and J.-P. Lessard. Computational fixed point theory for differential delay equations with multiple time lags. Journal of Differential Equations, 252 (4): 3093–3115, 2012. (pdf) The codes associated to this work can be found here.

[9] J.B. van den Berg, J.-P. Lessard, J.D. Mireles James and K. Mischaikow. Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation. SIAM Journal on Mathematical Analysis, 43 (4): 1557–1594, 2011. (pdf) The codes associated to this work can be found here.

[8] M. Gameiro and J.-P. Lessard. Existence of secondary bifurcations or isolas for PDEs. Nonlinear Analysis: Theory, Methods and Applications, 74 (12): 4131–4137, 2011. (pdf)

[7] M. Gameiro and J.-P. Lessard. Rigorous computation of smooth branches of equilibria for the three-dimensional Cahn-Hilliard equation. Numerische Mathematik, 117 (4): 753–778, 2011. (pdf)

[6] M. Gameiro and J.-P. Lessard. Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs. Journal of Differential Equations, 249 (9): 2237–2268, 2010. (pdf)

[5] J.B. van den Berg, J.-P. Lessard and K. Mischaikow. Global smooth solution curves using rigorous branch following. Mathematics of Computation, 79 (271), 1565–1584, 2010. (pdf)

[4] J.-P. Lessard. Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright’s equation. Journal of Differential Equations, 248 (5): 992–1016, 2010. (pdf) The codes associated to this work can be found here.

[3] J.B. van den Berg and J.-P. Lessard. Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. SIAM Journal on Applied Dynamical Systems, 7 (3): 988–1031, 2008. (pdf)

[2] M. Gameiro, J.-P. Lessard and K. Mischaikow. Validated continuation over large parameter ranges for equilibria of PDEs. Mathematics and computers in simulation, 79 (4): 1368–1382, 2008. (pdf)

[1] S. Day, J.-P. Lessard and K. Mischaikow. Validated continuation for equilibria of PDEs. SIAM Journal on Numerical Analysis, 45 (4): 1398–1424, 2007. (pdf)

THÈSES

J.-P. Lessard. Validated continuation for infinite dimensional problems. Ph.D. thesis, Georgia Institute of Technology, 2007. (pdf)

J.-P. Lessard. Bifurcations et chaos dans le système de Lorenz. M.Sc. thesis, Université de Montréal, 2002. (pdf)