7 Result(s)
within
Jean-Philippe Lessard
English
Partial Differential Equations
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Article
A General Method for Computer-Assisted Proofs of Periodic Solutions in Delay Differential Problems
In this paper we develop a general computer-assisted proof method for periodic solutions to delay differential equations. The class of problems considered includes systems of delay differential equations with ...
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Article
Parameterization of Unstable Manifolds for DDEs: Formal Series Solutions and Validated Error Bounds
This paper studies the local unstable manifold attached to an equilibrium solution of a system of delay differential equations (DDEs). Two main results are developed. The first is a general method for computin...
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Article
A Rigorous Implicit \(C^1\) Chebyshev Integrator for Delay Equations
We present a new approach to validated numerical integration for systems of delay differential equations. We focus on the case of a single constant delay though the method generalizes to systems with multiple ...
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Article
Parameterization of Invariant Manifolds for Periodic Orbits (II): A Posteriori Analysis and Computer Assisted Error Bounds
In this paper we develop mathematically rigorous computer assisted techniques for studying high order Fourier–Taylor parameterizations of local stable/unstable manifolds for hyperbolic periodic orbits of analy...
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Article
Rapidly and Slowly Oscillating Periodic Solutions of a Delayed Van der Pol Oscillator
In this paper, we introduce a method to prove existence of several rapidly and slowly oscillating periodic solutions of a delayed Van der Pol oscillator. The proof is a combination of pen and paper analytic es...
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Article
Computer Assisted Proof of Transverse Saddle-to-Saddle Connecting Orbits for First Order Vector Fields
In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously comput...
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Article
Global Bifurcation Diagrams of Steady States of Systems of PDEs via Rigorous Numerics: a 3-Component Reaction-Diffusion System
In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol. 53(4):617–641, 2006] to s...
