Canards in modified equations for Euler discretizations
Authors: Maximilian Engel, Georg A. Gottwald
Summary: Canards are a well-studied phenomenon in fast-slow peculiar differential equations implying the delayed lack of stability after the gradual passage by a singularity. Latest research have proven that the corresponding maps stemming from specific Runge-Kutta discretizations, particularly the ahead Euler scheme, exhibit important distinctions to the continuous-time habits: for folds, the delay in lack of stability is often shortened whereas, for transcritical singularities, it’s arbitrarily extended. We make use of the tactic of modified equations, which correspond with the mounted discretization schemes as much as larger order, to know and quantify these results instantly from a fast-slow ODE, yielding constant outcomes with the discrete-time habits and opening a brand new perspective on the wide selection of (de-)stabilization phenomena alongside canards
