HOODESolver.jl: A Julia package for highly oscillatory problems. Highly oscillatory ordinary di erential equations (ODEs) have a long history since they are ubiquitous to describe dynamical multi-scale physical phenomena in physics or chemistry. They can be obtained by an appropriate spatial discretization of partial di erential equations or can directly describe the behavior of dynamical quantities. In addition to the standard di culties relating to their numerical resolution, highly oscillatory ODEs involve a sti ness (characterized by a parameter ε ∈ ]0, 1]) which gives rise to high oscillations in the solution. Hence, to capture these small scales (or high oscillations), conventional methods have to consider a time step smaller than ε leading to unacceptable computational cost. We present here HOODESolver.jl1, a general-purpose library written in Julia dedicated to the e cient resolution of highly oscillatory ODEs. In the documentation2 details are given to explain how to simulate highly oscillatory ODEs using a Uniformly Accurate (UA) method ie a method which is able to capture the solution while keeping the time step (and then the computational cost) independent of the degree of sti ness ε.

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  1. Yves Mocquard; Pierre Navaro; Nicolas Crouseilles: HOODESolver.jl: A Julia package for highly oscillatory problems (2021) not zbMATH