To approximate the trajectories of a stochastic process by the solution of
some differential equation is widely used in the fields of probability,
computer science and combinatorics. In this paper, the convergence of coupon
collecting processes is studied via the differential equation techniques
originally proposed in Wormald(1995) and modified in Warnke(2019). In other
words, we give a novel approach to analysis the classical coupon collector's
problem and keep track of all coupons in the process of collecting