  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.
