riccati: an adaptive, spectral solver for oscillatory ODEs

Abstract

Highly oscillatory ordinary differential equations (ODEs) pose a computational challenge for standard solvers available in scientific computing libraries. These conventional methods are typically based on a polynomial approximation, resulting in there being several timesteps per oscillation period, which leads to runtimes scaling as 𝒪(𝜔), with 𝜔 being the oscillation frequency. This can become prohibitively slow.