Browsing by Author "Lessard, J.-P."
Now showing items 1-7 of 7
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Computational fixed-point theory for differential delay equations with multiple time lags
Kiss, G.; Lessard, J.-P. (2012-12-31)We introduce a general computational fixed-point method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of ... -
Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates
Gameiro, M.; Lessard, J.-P. (2013-12-31)We present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential ... -
Existence of secondary bifurcations or isolas for PDEs
Gameiro, M.; Lessard, J.-P. (2011-12-31)In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ... -
Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form
Castelli, R.; Lessard, J.-P.; James, J.D.M. (2015-12-31)We present an efficient numerical method for computing Fourier-Taylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. Three features of the method are that (1) we obtain accurate representation ... -
Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation
Gameiro, M.; Lessard, J.-P. (2011-12-31)In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higher-dimensional partial differential equations. The theoretical framework is based on a combination of the ... -
Rigorous numerics for symmetric connecting orbits: Even homoclinics of the Gray-Scott equation
Van Den Berg, J.B.; Mireles-James, J.D.; Lessard, J.-P.; Mischaikow, K. (2011-12-31)In this paper we propose a rigorous numerical technique for the computation of symmetric connecting orbits for ordinary differential equations. The idea is to solve a projected boundary value problem (BVP) in a function ... -
Rigorous numerics in floquet theory: Computing stable and unstable bundles of periodic orbits
Castelli, R.; Lessard, J.-P. (2013-12-31)In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of nonautonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental ...