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A new linear and conservative finite difference scheme for the Gross-Pitaevskii equation with angular momentum rotation. (English) Zbl 1415.65189
Summary: 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.
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Software:
GPELab
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