Wiktionary
vb. (context idiomatic English) To create in one’s mind; to invent.
WordNet
Usage examples of "think up".
The warlock made out the conferral in the name of Lord Eshern, so Ylo will be Lord Eshern and we shall have to think up another name for you.
He could think up his own reasons for keeping this sign, without help from the Mead-memories.
Her modifications in the way of fingers and enlarged brain gave her no real qualification to think up to man's level.
If given a free hand they will think up so marry interlocking relationships and lines of authority and committees, and ordain so many committee meetings and consultations and memoranda in octuplicate, that the organization will be paralyzed by sheer complexity.
From here, strange people like Jess and strange places like the slum they called dirtside and man-eating corporations called ETORP seemed like something you'd think up in the dark hours of the night after too much lobster and fruitcake.
I had maybe thirty seconds to think up a scheme, check it over for flaws, and put it into execution.