7 Result(s)
within
Jean-Philippe Lessard
Mathematics
Theoretical, Mathematical and Computational Physics
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Article
Open AccessSaddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining...
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Article
Open AccessCorrection to: Rigorous numerics for nonlinear heat equations in the complex plane of time
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Article
Open AccessRigorous numerics for nonlinear heat equations in the complex plane of time
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explici...
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Article
Spontaneous Periodic Orbits in the Navier–Stokes Flow
In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier–Stokes equations on the three-torus is proposed. After introducing a zero finding p...
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Article
Computing Discrete Convolutions with Verified Accuracy Via Banach Algebras and the FFT
We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this ne...
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Article
Analytic enclosure of the fundamental matrix solution
This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form...
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Article
Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation
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 combinati...
