3 papers
math.AP2026
Rigorous Validation of Cusp Bifurcations of Stationary Periodic Patterns in Partial Differential Equations
Dominic Blanco, Jean-Philippe Lessard
In this paper, we present a computer-assisted framework for the rigorous validation of cusp bifurcations of spatially symmetric stationary periodic patterns in parabolic semilinear…
math.AP2025
Recent advances about the rigorous integration of parabolic PDEs via fully spectral Fourier-Chebyshev expansions
Matthieu Cadiot, Jean-Philippe Lessard
This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebys…
math.NA2024
Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard +1
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First,…