Force the timestep option to be 1/2 of the spacestep option, and it always seems to "work", irrespective of the magnitude of the latter.
The attached works for all values of "myStep" which I have tried.
I could speculate on why - so (at the risk of being completely wrong). SInce the spatial domain is symmetrical wrt 0, a spacestep setting of 0.1, would give 20 intervals. To guarantee 20 intervals in time, the timestep has to be set to 0.05. Maybe when computing a "default" timestep, Maple just uses the spacestep setting (ie 0.1), ignoring the spatial range, and thus ends up with 10 time intervals?
In general things seem to work better if the number of time intervals = number of spatial intervals
PS I also "corrected" the definition of the piecewise function used for the initial conditions, because I didin't understand wht yo menat by the condition 'true', and it was undefined for x=0
Anyhow for what it is worth the attached seems to work OK.