Three higher-accurate boundary conditions is introduced. The first-order spacial differential is calculated by using the Spline function,and a set of simpler calculating formulation of the Hermite method is presented. Comparisons of the interpolation errors among the Lagrangian,the Spline and the Hermite schemes for different locations of the interpolation points are made. The results show that although these schemes have given accuracies to some extent,the error of the Hermite method with periodic boundary condition is around one fourth or a half of the errors of other boundary conditions,and is about one order of magnitude smaller than that of the Lagrangian technique.