A fully discrete low-regularity integrator for the nonlinear Schrödinger equation

2021/08/10 by Alexander Ostermann, Ostermann, Alexander, Fangyan Yao +1 · 1 citation
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Advanced Mathematical Physics Problems #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2108.04794

Abstract

For the solution of the cubic nonlinear Schrödinger equation in one space dimension, we propose and analyse a fully discrete low-regularity integrator. The scheme is explicit and can easily be implemented using the fast Fourier transform with a complexity of O(Nlog N) operations per time step, where N denotes the degrees of freedom in the spatial discretisation. We prove that the new scheme provides an O(τ^{\frac32γ-\frac12-ε}+N^-γ) error bound in L² for any initial data belonging to H^γ, \frac12

Cited by

• Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation

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