How to let go of doubt?

I have a question which has probably been answered before, but I'm unable to find it. Sorry about that. My mind is unfortunately very logically driven. My question is, is doubt removed after making progress, or is it up to me to remove the doubt? I want to not doubt, but I cannot help to doubt. I practice meditation often and a common thought is "am I wasting my time?" I know I am not, but the thought still arises. Do I just accept the doubtful thoughts, or do I try and transform them? Many thanks!