This paper presents an optimal conflict resolution method for multiple unmanned aerial vehicles based on pseudospectral collocation which solves numerically optimal control problems by using non-linear programming. The trajectory of each aerial vehicle is defined by a set of waypoints and the time of arrival at each waypoint. The maneuvers allowed to solve the conflicts are the changes of speed of each aerial vehicle. A novel aspect is the application of this kind of methods to multiple aerial vehicles. The main characteristic of the method is the low execution time in the addressed problem. Moreover, the scalability of the proposed method is studied and the execution time is compared with another optimal solver. Several simulations in different scenarios are performed to test the behavior of the method.