3 papers
math.DS2022
Nonlinear stability of shock-fronted travelling waves under nonlocal regularization
Ian Lizarraga, Robert Marangell
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied b…
math.DS2020
Contact singularities in nonstandard slow-fast dynamical systems
Ian Lizarraga, Robert Marangell, Martin Wechselberger
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form , and $\varepsilon\l…
math.DS2019
Computational singular perturbation method for nonstandard slow-fast systems
Ian Lizarraga, Martin Wechselberger
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since it…