Convergent analysis of energy conservative algorithm for the nonlinear Schrödinger equation (Q1666516)

Summary: 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 discrete \(L_2\) norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.