Particle trajectory in time on the axis of a magnetic bottle. There is no observable difference after 10 cycles through the magnetic bottle between all methods and the GCA results, here shown for the run with interpolated fields and time step ﹩{\rm{\Delta }}t={10}^{-8}﹩ for all methods, except for the Vay method, where we had to use ﹩{\rm{\Delta }}t={10}^{-9}﹩ for the particle not to escape the magnetic bottle. For all methods, the particle stays within the analytically predicted range ﹩{z}_{\max }=\pm {10}^{7}﹩.