Before discovering the relation between meditation and non-violence it is necessary to find out the root cause of violence, as also the factors which provide sustenance to violence. One of the most important factors is stress. Violence is not possible in the absence of stress. A relaxed person cannot commit violence. The muscles get tense, the mind becomes tense and the feelings turn tense too.
Violence is the natural outcome.
Basically, of course most tension is born of an agitated mind. Whatever the provenance, all types of tensions generate violence. A hurt ego can spell disaster, so can the passions of anger and greed. Similarly, desperation and defeat can also result in violence, as is the case with most suicides. Against the backdrop of tension or stress, it becomes meaningful to talk about meditation and non-violence.