8 citations · 14 across the 6 of their papers we have counts for
8 papers
Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof
Maxime Breden, Roberto Castelli
In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation pro…
The monotonicity of the apsidal angle in power-law potential systems
R. Castelli
In a central force system the apsidal angle is the angle at the centre of force between two consecutive apsis and measures the precession rate of the line of apsis. The apsidal ang…
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
R. Castelli, M. Gameiro, J. -P. Lessard
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is appl…
Rigorous numerics for NLS: bound states, spectra, and controllability
Roberto Castelli, Holger Teismann
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound--state solutio…
A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case
Roberto Castelli
This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree and logarithmic potential. We derive…
A method to rigorously enclose eigendecompositions of interval matrices
Roberto Castelli, Jean-Philippe Lessard
In this paper, a rigorous computational method to enclose eigendecompositions of complex interval matrices is proposed. Each eigenpair is found by solving a nonlinear equ…