Two numerical schemes are proposed for solving the Degasperis-Procesi equation.One method is the symplectic pseudospectral Fourier spectral integrator,and the other is constructed by the splitting technique.Using the two schemes,we compute the three classes of solutions: smooth solution,peakon solution and shock wave solution.We show the good behavior of the scheme by the splitting method in simulating the shock wave solution,and compute numerically the convergence order.