Optimal H<sup>1</sup>-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term

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.

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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.