Optimal H1-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term

East Asian Journal on Applied Mathematics
Vol. 8 No. 3 (2018), pp. 385-398
DOI: 10.4208/eajam.060218.270418
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Author(s)
    Jin Cui
    Nanjing Normal Univ, Sch Math Sci, Jiangsu Prov Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China Nanjing Vocat Coll Informat Technol, Dept Basic Sci, Nanjing 210023, Jiangsu, Peoples R China
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1 Nanjing Normal Univ, Sch Math Sci, Jiangsu Prov Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China
2 Nanjing Vocat Coll Informat Technol, Dept Basic Sci, Nanjing 210023, Jiangsu, Peoples R China
Received
February 6, 2018
Accepted
April 27, 2018
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.

Keywords
Gross-Pitaevskii equation with angular momentum rotation finite difference method conservation laws error estimate.
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