  Particle-in-cell codes are now standard tools for studying ultra-intense
laser-plasma interactions. Motivated by direct laser acceleration of electrons
in sub-critical plasmas, we examine temporal resolution requirements that must
be satisfied to accurately calculate electron dynamics in strong laser fields.
Using the motion of a single electron in a perfect plane electromagnetic wave
as a test problem, we show surprising deterioration of the numerical accuracy
with increasing wave amplitude $a_0$ for a given time-step. We go on to show
analytically that the time-step must be significantly less than $\lambda/c a_
0$ to achieve good accuracy. We thus propose adaptive electron sub-cycling as
an efficient remedy.
