I present a pseudospectral explicit scheme that can simulate low-frequency electromagnetic (EM) propagation in the earth. This scheme solves linear periodic parabolic equations, having accuracy within machine precision, both temporally and spatially. The method is based on a Chebyshev expansion of the evolution operator, with the spatial derivatives computed via a staggered Fourier pseudospectral technique. The results match analytical solutions of the initial-value problem and the Green's function. An example of the EM field produced by a set of magnetic sources in a heterogeneous model illustrates the algorithm's performance.