TY - JOUR
T1 - An Extended Fourier Pseudospectral Method for the Gross-Pitaevskii Equation with Low Regularity Potential
AU - Bao , Weizhu
AU - Lin , Bo
AU - Ma , Ying
AU - Wang , Chushan
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 530
EP - 550
PY - 2024
DA - 2024/05
SN - 14
DO - http://doi.org/10.4208/eajam.2023-273.010124
UR - https://global-sci.org/intro/article_detail/eajam/23160.html
KW - Gross-Pitaevskii equation, low regularity potential, extended Fourier pseudospectral method, time-splitting method, optimal error bound.
AB - <p style="text-align: justify;">We propose and analyze an extended Fourier pseudospectral (eFP) method
for the spatial discretization of the Gross-Pitaevskii equation with low regularity potential by treating the potential in an extended window for its discrete Fourier transform.
The proposed eFP method maintains optimal convergence rates with respect to the regularity of the exact solution even if the potential is of low regularity and enjoys similar computational cost as the standard Fourier pseudospectral method, and thus it is
both efficient and accurate. Furthermore, similar to the Fourier spectral/pseudospectral
methods, the eFP method can be easily coupled with different popular temporal integrators including finite difference methods, time-splitting methods and exponential-type
integrators. Numerical results are presented to validate our optimal error estimates and
to demonstrate that they are sharp as well as to show its efficiency in practical computations.</p>