Discarding the canonical magnetohydrodynamic approximation frees the magnetic field to diffuse with respect to the bulk velocity field. As a consequence the induction equation becomes problematic to solve numerically via standard explicit techniques. In particular, the Hall diffusion term can impose vanishing timestep limits on conventional explicit schemes. We present two complementary techniques to alleviate the problems of a diffusion‐like stability limit from within an explicit differencing framework.

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