 Substitution method for a recurrence

Prove a proposed bound by mathematical induction, substituting the inductive hypothesis for smaller arguments into the recurrence relation. Choose its constants so the resulting inequality implies the proposed bound at the current argument, and verify all base cases. A leading-order guess may need an additional lower-order term to make the induction close. The entropy potential for a divide-and-conquer recurrence is an example using a linear correction to an $n\log n$ bound.