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Volume 8, Issue 3
Optimal H1-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term

Jin Cui, Chaolong Jiang & Yushun Wang

East Asian J. Appl. Math., 8 (2018), pp. 385-398.

Published online: 2018-08

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  • 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.

  • AMS Subject Headings

65M06, 65M12

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-385, author = {Jin Cui, Chaolong Jiang and Yushun Wang}, 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} }
TY - JOUR T1 - Optimal H1-Error Estimates for Crank-Nicolson Finite Difference Scheme for Gross-Pitaevskii Equation with Angular Momentum Rotation Term AU - Jin Cui, Chaolong Jiang & Yushun Wang 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 -

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.

Jin Cui, Chaolong Jiang and Yushun Wang. (2018). 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. 8 (3). 385-398. doi:10.4208/eajam.060218.270418
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