A new linear and conservative finite difference scheme for the Gross–Pitaevskii equation with angular momentum rotation

Jin Cui, Wenjun Cai, Chaolong Jiang, Yushun Wang


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 \(O(h^4+\tau^2)\) with time step \(\tau\) and mesh size \(h\). Numerical experiments have been carried out to show the efficiency and accuracy of our new method.



Gross–Pitaevskii equation, angular momentum rotation, finite difference scheme, conservation law, error estimate.

DOI: http://dx.doi.org/10.21914/anziamj.v61i0.13426

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.