@Article{EAJAM-8-385, author = {}, title = {Optimal H1-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {3}, pages = {385--398}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.060218.270418}, url = {http://global-sci.org/intro/article_detail/eajam/12614.html} }