I'm doing some particle-in-cell (PIC) simulations of propagation of short pulses in plasmas with a widely used code. This code uses Yee's field solver. So, the timestep must be lower than the Courant limit. But the question is: How much? In one published work I read that a value much smaller than the Courant limit can cause numerical errors in PIC simulation.
In my own experience the simulation results for a timestep of ~90% of the Courant limit and for a timestep of ~50% are significantly different. An experienced physicist doing these kinds of simulations told me that I should use a timestep of ~90% of the Courant limit. But then, how can the significant difference that I just mentioned be understood?