We present in this paper some especial procedures for the numerical solution of the optimal schedule problem of a multi-item single machine. A method of discretization and a computational procedure are described which allows us to calculate the solution in a short time and with a precision of order k, being k the size of the discretization. The principal feature of this method is the fact that the nodes of the triangulation mesh are joined by segments of trajectories of the original system. This feature allows us to obtain the k-order precision which, in general, is impossible to obtain by usual methods. We also develop a highly efficient algorithm that converges in a finite number of steps.