How to prevent water coming off the edge of a roof with no gutter?
That edge of your roof is called the “rake” edge. 

Water is probably running off it because 1) it’s slightly lower than the main roof, or 2) heavy rain and wind pushes it off that edge. 

To keep the water from coming off the rake edge, is recommend a “standing seam” edge. The height will depend on how much rain you get and the length of the rake edge. 

Here, we get a lot of rain all at once and we use a 3/4” to 1” high standing ridge at the edge, depending on the length of run.