encourage and stimulate

Encourage means to give somebody support, courage or hope. Or to persuade someone to do something by making it easier for them and making them believe it is a good thing to do.
Stimulate means to make something develop or become more active, or to encourage something.

encourage
vt.
1. 鼓勵;慫恿[O2]
She encouraged him to talk to her.
她鼓勵他與她交談。
2. 促進,助長;激發
Don't encourage her laziness by doing things for her.
別替她做事,這會助長她的懶惰。
3. 支持

stimulate

vt.
1. 刺激;激勵;使興奮;促使[(+to/into)][O2]
The government will do everything in its power to stimulate economic growth.
政府將竭盡全力去刺激經濟發展。
2. 促進...的功能
The optical system of the eye stimulates cells of the retina.
眼睛的視覺系統刺激視網膜內的細胞。
Exercise stimulates the flow of blood.
運動促進血液循環。
vi.
1. 有刺激之作用;起促進作用