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

Lan Wang, Wenjun Cai & Yushun Wang

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 = {Lan and Wang and and 9407 and and Lan Wang and Wenjun and Cai and and 9408 and and Wenjun Cai and Yushun and Wang and and 9409 and and Yushun Wang}, 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.

Lan Wang, Wenjun Cai & Yushun Wang. (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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