Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field

TL;DR

This paper develops uniformly accurate numerical methods for solving highly-oscillatory Vlasov equations with non-homogeneous magnetic fields, effectively handling non-periodic oscillations and maintaining efficiency regardless of problem stiffness.

Contribution

The paper introduces novel schemes that are insensitive to stiffness and specifically address non-periodic oscillations in Vlasov equations with non-homogeneous magnetic fields.

Findings

Methods remain accurate regardless of oscillation frequency.

Numerical examples demonstrate effectiveness and efficiency.

Approach handles non-periodic oscillations successfully.

Abstract

In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to the stiffness of the problem, in terms of both accuracy and computational cost. The specific difficulty (and the resulting novelty of our approach) stems from the presence of a non-periodic oscillation, which necessitates a careful ad-hoc reformulation of the equations. Our results are illustrated numerically on several examples.