Optimal H<sup>1</sup>-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.060218.270418
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 385–398
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Gross-Pitaevskii equation with angular momentum rotation finite difference method conservation laws error estimate.