The simulation of whistler waves in cold electron plasma is the main subject of this well-written, comprehensive paper. Gumerov et al. consider waves generated by loop antennas, as well as spheromak-like stationary waves. The solution that they propose is based on newly proposed spectral and pseudospectral algorithms.

A deep analysis shows the linear stability of the algorithms and their acceptable stability properties in the difficult nonlinear 3D case. Complex tests are related to the numerical, as well as the exact, solution in particular cases. The comparisons with the experimental results and the visual representations certify the appropriateness of the proposed approach.

Moreover, the authors conduct tests using both central processing units (CPUs) and graphics processing units (GPUs). The case using GPUs reveals a considerable speedup.

Specialists in simulation, as well the those involved in parallel computing, will find this paper relevant for their activities. Moreover, it is an example of a complete cycle of work: the problem, the model, the algorithms, the proof of correctness, the comparison with experimental results, and the performance studies.