A numerical method to reduce the computing times of thin-film flows with moving contact lines is presented. The flows of a film and a droplet are calculated in a frame that moves with a nonconstant velocity U(t). The criterion employed to define this velocity is to reduce the maximum height change in the flow's most critical zone. The efficiency of the algorithm in reducing the CPU time is tested in gravity-driven flows, where the computing time is reduced by up to a factor of 13 depending on the parameters of the problem.