13 citations · 24 across the 12 of their papers we have counts for
20 papers
Validation of Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems
Maxime Breden, Evelyn Sander, Thomas Wanner
Nonlinear parabolic partial differential equations frequently occur in the modeling of applied phenomena. They often exhibit complicated dynamics which is organized by their associ…
Efficient Rigorous Continuation via Chebyshev Series Expansion I
Maxime Breden, Olivier Hénot
We study the global continuation of solution manifolds arising in dynamical systems. We present a rigorous continuation method based on a Chebyshev series expansion of the solution…
A simple rigorous integrator for semilinear parabolic PDEs
Jan Bouwe van den Berg, Maxime Breden
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous i…
Validated integration of semilinear parabolic PDEs
Jan Bouwe van den Berg, Maxime Breden, Ray Sheombarsing
Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scienti…
A posteriori validation of generalized polynomial chaos expansions
Maxime Breden
Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invar…
Computer-assisted proofs for some nonlinear diffusion problems
Maxime Breden
In the last three decades, powerful computer-assisted techniques have been developed in order to validate a posteriori numerical solutions of semilinear elliptic problems of the fo…