An algorithm and data structures are developed for finding the solution to the nonlinear finite time optimal control problems based on double generating functions. The optimal state and input trajectories are given in the forms of Taylor series with respect to the initial and the terminal values of the state. Therefore, it is easy to generate a family of optimal state and input trajectories for different boundary conditions. The proposed algorithm furnishes a systematic procedure to compute the coefficients of the Taylor series solution recursively up to any order off-line. The on-demand computational effort decreases greatly compared with the conventional method.