(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
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.