TY - JOUR
T1 - A Second-Order Embedded Low-Regularity Integrator for the Quadratic Nonlinear Schrödinger Equation on Torus
AU - Yao , Fangyan
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 656
EP - 668
PY - 2022
DA - 2022/08
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/20931.html
KW - Quadratic nonlinear Schrödinger equation, low-regularity integrator, second-order convergence, fast Fourier transform.
AB - <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>