一个高效求解含时Gross-Pitaevskii方程的算法

An efficient algorithm for solving time-dependent Gross-Pitaevski equation

Gross-Pitaevskii方程广泛应用于玻色-爱因斯坦凝聚体(Bose-Einstein condensate,BEC)的动力学研究,然而这个方程通常很难解析求解.因此发展相应的高精度数值求解方法非常重要.发展了结合算符劈裂法、Crank-Nicolson算法和四阶精度Numerov算法的高效求解Gross-Pitaevskii方程的新数值计算方法.通过数值计算可以表明,与传统的四阶精度的五点差分法相比,所提出的算法具有高效和消耗内存小的优点.

The Gross-Pitaevskii equation is widely applied in Bose-Einstein condensate research,yet is rarely analytically determined;thus,it is important to develop a numerical method with high precision to resolve this.Accordingly,a numerical method was developed in this work,considering the splitting step method,Crank-Nicolson algorithm,and Numerov algorithm with four-order accuracy.The corresponding test shows that compared with the finite difference method using five points,the proposed algorithm is more efficient and costs less memory.