@Article{IJNAM-19-5,
author = {Yao, Fangyan},
title = {A Second-Order Embedded Low-Regularity Integrator for the Quadratic Nonlinear Schrödinger Equation on Torus},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2022},
volume = {19},
number = {5},
pages = {656--668},
abstract = {<p style="text-align: justify;">A new embedded low-regularity integrator is proposed for the quadratic nonlinear
Schrödinger equation on the one-dimensional torus. Second-order convergence in $H^\gamma$ is proved
for solutions in $C([0, T]; H^\gamma)$ with $\gamma &gt; \frac{3}{2},$ i.e., no additional regularity in the solution is required.
The proposed method is fully explicit and can be computed by the fast Fourier transform with $\mathcal{(O} log N)$ operations at every time level, where $N$ denotes the degrees of freedom in the spatial
discretization. The method extends the first-order convergent low-regularity integrator in [14] to
second-order time discretization in the case $\gamma &gt;\frac{3}{2}$ without requiring additional regularity of the
solution. Numerical experiments are presented to support the theoretical analysis by illustrating
the convergence of the proposed method.</p>},
issn = {2617-8710},
doi = {https://doi.org/2022-IJNAM-20931},
url = {https://global-sci.com/article/82953/a-second-order-embedded-low-regularity-integrator-for-the-quadratic-nonlinear-schrodinger-equation-on-torus}
}