Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discreteL2norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.