2维Gross-Pitaevskii方程的分裂高阶紧致差分格式

该文为带有旋转角动量的Gross-Pitaevskii方程构造了分裂高阶紧致差分格式.首先通过时间分裂将其分为线性方程和非线性方程,非线性方程可以通过质量守恒定律进行精确求解,线性方程通过高阶紧致格式和局部1维方法进行离散,最终得到的格式时间方向2阶收敛和空间方向4阶收敛,并保持质量守恒.最后用数值算例验证了格式的收敛阶以及质量守恒性.

The Splitting High-Order Compact Difference Scheme for Two-Dimensional Gross-Pitaevskii Equation

The splitting high-order compact difference scheme for the Gross-Pitaevskii equation with angular momentum rotation term is constructed.Firstly,the equation is divided into linear equations and nonlinear equations by time splitting method.Secondly,the nonlinear equations can be accurately solved by the conservation law of mass,and the linear equation is discretized by a high-order compact scheme and a local one-dimensional method.The resulting scheme converges second-order in time and fourth-order in space while maintaining mass conservation.Finally,numerical experiments verify the convergence orders and mass conservation of the scheme.