think of vs think up

think of and think up both are verbs.

Word	Noun	Adjective	Verb	Adverb
think of	No	No	Yes	No
think up	No	No	Yes	No

As verbs, think of and think up are synonyms defined as:

Other synonyms of think of include concoct, dream up, hatch.

think of (verb)	think up (verb)
keep in mind for attention or consideration	devise or invent
look on as or consider
intend to refer to
take into consideration, have in view
choose in one's mind
devise or invent