A conservative scheme for two-dimensional Schrödinger equation based on multiquadric trigonometric quasi-interpolation approach

作者：

Highlights：

• Based on multiquadric trigonometric quasi-interpolation method, a simple mass and energy conservative scheme is proposed for solving the two-dimensional Schrödinger equation.

• To preferably process the (L1,L2)-periodic boundary conditions, a tensor-product periodic kernel is employed in the construction of quasi-interpolation method. Moreover, two different approaches are presented to approximate high order derivatives. The salient properties of differentiation matrices are explored.

• The convergence of new conservative scheme is given in detail. Furthermore, compared with traditional conservative methods, the proposed method can preserve the mass and energy for nonuniform grids.

摘要

•Based on multiquadric trigonometric quasi-interpolation method, a simple mass and energy conservative scheme is proposed for solving the two-dimensional Schrödinger equation.•To preferably process the (L1,L2)-periodic boundary conditions, a tensor-product periodic kernel is employed in the construction of quasi-interpolation method. Moreover, two different approaches are presented to approximate high order derivatives. The salient properties of differentiation matrices are explored.•The convergence of new conservative scheme is given in detail. Furthermore, compared with traditional conservative methods, the proposed method can preserve the mass and energy for nonuniform grids.

论文关键词：Quasi-interpolation,Schrödinger equation,Multiquadric function,Conservative schemes

论文评审过程：Received 17 September 2021, Revised 15 December 2021, Accepted 29 January 2022, Available online 12 February 2022, Version of Record 12 February 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.126996