TY - JOUR
T1 - Optimal H<sup>1</sup>-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 385
EP - 398
PY - 2018
DA - 2018/08
SN - 8
DO - http://doi.org/10.4208/eajam.060218.270418
UR - https://global-sci.org/intro/article_detail/eajam/12614.html
KW - Gross-Pitaevskii equation with angular momentum rotation, finite difference method,
conservation laws, error estimate.
AB - <p style="text-align: justify;">Optimal $H^1$-error estimates for a Crank-Nicolson finite difference scheme for
2D-Gross-Pitaevskii equation with angular momentum rotation term are derived. The
analysis is based on classical energy estimate method and on the lifting technique. With
no constraint on the grid ratio, we show that the convergence rate of approximate solutions
is equivalent to $O$($τ^2$+$h^2$), consistent with numerical results of the existing
studies.</p>