具有非均匀强磁场的Vlasov方程的均匀准确方法
Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field
AI总结：
本文提出了一种适用于高振荡Vlasov和Vlasov-Poisson方程的数值求解方法，该方法在准确性和计算成本上对问题的刚性不敏感，通过非周期性振荡的特殊处理实现了方法的创新。
摘要：
在本文中，我们考虑了具有非均匀磁场的高振荡Vlasov和Vlasov-Poisson方程的数值解法。在近期均匀准确方法的精神指导下，我们的方案在准确性和计算成本上均对问题的刚性不敏感。具体困难（也是我们方法的创新点）源于非周期性振荡的存在，这需要对方程进行仔细的特制改写。我们的结果在几个例子上进行了数值验证。
英文摘要：
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.
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