  Response functions of resonant circuits create ringing artefacts if their
input changes rapidly. When physical limits of electromagnetic spectroscopies
are explored, this creates two types of problems. Firstly, simulation: the
system must be propagated accurately through every response transient, this may
be computationally expensive. Secondly, optimal control: circuit response must
be taken into account; it may be advantageous to design pulses that are
resilient to such distortions. At the root of both problems is the popular
piecewise-constant approximation for control sequences in the rotating frame;
in magnetic resonance it has persisted since the earliest days and has become
entrenched in the commercially available hardware. In this paper, we report an
implementation and benchmarks of recent Lie-group methods that can efficiently
simulate and optimise smooth control sequences.
