Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

Abstract EN

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.