High-order splitting integrators for nonlinear Schrödinger equations over long times
Provides theoretical guarantees for long-time stability of numerical methods for nonlinear Schrödinger equations, relevant to computational physics and numerical analysis.
The paper proves that high-order splitting integrators nearly conserve energy over long times for nonlinear Schrödinger equations in a weakly nonlinear regime, with rigorous error bounds.
The long-time behaviour of splitting integrators applied to nonlinear Schrödinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserved on long time intervals. The analysis includes all consistent splitting integrators with real-valued coefficients, in particular splitting integrators of high order. The proof is based on a completely resonant modulated Fourier expansion in time of the numerical solution.