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- W4242632777 abstract "A new linear and conservative finite difference scheme which preserves discrete mass and energy is developed for the two-dimensional Gross–Pitaevskii equation with angular momentum rotation. In addition to the energy estimate method and mathematical induction, we use the lifting technique as well as some well-known inequalities to establish the optimal $H^{1}$ -error estimate for the proposed scheme with no restrictions on the grid ratio. Unlike the existing numerical solutions which are of second-order accuracy at the most, the convergence rate of the numerical solution is proved to be of order $O(h^{4}+unicode[STIX]{x1D70F}^{2})$ with time step $unicode[STIX]{x1D70F}$ and mesh size $h$ . Numerical experiments have been carried out to show the efficiency and accuracy of our new method." @default.
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- W4242632777 date "2019-04-01" @default.
- W4242632777 modified "2023-10-16" @default.
- W4242632777 title "A NEW LINEAR AND CONSERVATIVE FINITE DIFFERENCE SCHEME FOR THE GROSS–PITAEVSKII EQUATION WITH ANGULAR MOMENTUM ROTATION" @default.
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- W4242632777 doi "https://doi.org/10.1017/s1446181119000026" @default.
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