This page regroups the contributions of David Fabre to the Easystab project. For info on my other research projects and my full list of publications, see [my professional page](https://www.imft.fr/FABRE-David-136) # Discretization methods * [dif1D.m]() Added a number of options (mapped chebyshev, etc...) -> integrated in main project * [differential_equation_fd_cheb.m]() Comparison of finite-difference and chebyshev (uses dif1D) -> to integrate in the main project * [differential_equation_infinitedomain.m]() Test of discretization methods for resolution of a problem in an infinite domain using mapped chebyshev -> to integrate in the main project # Dynamical systems * [PhasePortrait_NonLinear.m]() Draws phase portraits for an number of classical 2D dynamical systems (lokta-voltera, brusselator, van der pol, pendulum, ...) * [PhasePortrait_Linear.m]() Classification of equilibrium points for 2D problems * [Lorenz.m]() Lorenz system # Instability problems * [GinsburgLandau.m]() Demonstration of the numerical resolution of an instability problem for a sample 1D problem. In 2018/2019 this one was splitted in [GinsburgLandau_Linear.m]() and [GinsburgLandau_NonLinear.m]() * [wave_like_Psi.m]() Basic example of wave-like perturbations in a channel ; comparison between UVP formulation (primitive), Psi formulation (Orr-Sommerfeld), and theory for SLIP conditions at the wall. * [wave_like_Psi_noslip.m]() Same but modified for NO-SLIP conditions at the wall. * [RayleighBenard.m]() No-slip condition, including loops over parameters to draw the neutral curve. -> already integrated * [KH_temporal_inviscid.m]() Kelvin-Helmholtz for the tanh shear layer. Uses chebyshev method with coordinate stretching. -> To integrate in main project * [KH_temporal_viscous.m]() Same program in the viscous case. Plots a series of curves for various values of Re. -> To integrate in main project * [TS_PlanePoiseuille.m]() Plane poiseuille : includes loops over k and Re to draw the neutral curve -> to integrate in the main project * [KH_temporal_viscous.m]() # Lecture notes for the M2R-DET course The overview of the course is here : [M2RDET_2018.md]() Lecture notes for several chapters are available here : * [LinearSystems.md]() * [DynamicalSystems.md]() Other contributions (to be linked with the rest of the project) are :