TY - JOUR
T1 - Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions
AU - Kang , Shengnan
AU - Abdella , Kenzu
AU - Pollanen , Macro
AU - Zhang , Shuhua
AU - Wang , Liang
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1302
EP - 1332
PY - 2022
DA - 2022/08
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0189
UR - https://global-sci.org/intro/article_detail/aamm/20849.html
KW - Quantum mechanics, spectral method, time-dependent partial differential equation, boundary value problem.
AB - <p style="text-align: justify;">This paper presents the numerical solution of the time-dependent Gross-Pitaevskii Equation describing the movement of quantum mechanics particles under
non-homogeneous boundary conditions. Due to their inherent non-linearity, the equation generally can not be solved analytically. Instead, a highly accurate approximation to the solutions defined in a finite domain is proposed, using the Crank-Nicolson
difference method and Sinc Collocation numerical methods to discretize separately
in time and space. Two Sinc numerical approaches, involving the Sinc Collocation
Method (SCM) and the Sinc Derivative Collocation Method (SDCM), are easy to implement. The results demonstrate that Sinc numerical methods are highly efficient and
yield accurate results. Mainly, the SDCM decays errors faster than the SCM. Future
work suggests that the SDCM can be extensively applied to approximate solutions
under other boundary conditions to demonstrate its broad applicability further.</p>