There are situations where they could be interchangeable. That being said... Encouragement is more something someone gives you to push you along when you need a little help. Stimulation is when something excites you and keeps you interested. "She encouraged him to go out and talk to new people." - she pushes him in a direction "He found himself stimulated by the new conversation." - the conversation keeps his attention.

They both have the same meaning, and often be used interchangeably. Although I would use encourage when referring to people, e.g. "I encouraged him to keep improving"; and stimulate for more scientific contexts or for inanimate objects, e.g, "The presence of food stimulated bacterial growth". In these two sentences, it still makes sense if you switched encouraged and stimulated, but they are more appropriate in the context given.

encourage -- add courage