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Volume 13, Issue 1
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations

Lan Wang, Wenjun Cai & Yushun Wang

DOI: 10.4208/aamm.OA-2019-0308

Adv. Appl. Math. Mech., 13 (2021), pp. 203-231.

Published online: 2020-10

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  • Abstract

An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.  The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction, respectively. The scheme is energy-preserving, stable, and of sixth order in space and of second order in time. Numerical experiments verify the theoretical results. The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated.

  • Keywords

Coupled Gross-Pitaevskii equations, average vector field method, high order compact method, energy-preserving scheme.

  • AMS Subject Headings

65M06, 65M12, 65Z05, 70H15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-203, author = {Wang , LanCai , Wenjun and Wang , Yushun}, title = {An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {1}, pages = {203--231}, abstract = {

An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.  The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction, respectively. The scheme is energy-preserving, stable, and of sixth order in space and of second order in time. Numerical experiments verify the theoretical results. The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0308}, url = {http://global-sci.org/intro/article_detail/aamm/18348.html} }
TY - JOUR T1 - An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations AU - Wang , Lan AU - Cai , Wenjun AU - Wang , Yushun JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 203 EP - 231 PY - 2020 DA - 2020/10 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0308 UR - https://global-sci.org/intro/article_detail/aamm/18348.html KW - Coupled Gross-Pitaevskii equations, average vector field method, high order compact method, energy-preserving scheme. AB -

An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.  The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction, respectively. The scheme is energy-preserving, stable, and of sixth order in space and of second order in time. Numerical experiments verify the theoretical results. The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated.

Wang , LanCai , Wenjun and Wang , Yushun. (2020). An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations. Advances in Applied Mathematics and Mechanics. 13 (1). 203-231. doi:10.4208/aamm.OA-2019-0308
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