Convergent analysis of energy conservative algorithm for the nonlinear Schrödinger equation. (English) Zbl 1394.65115
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.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
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