Abstract:

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.

Key words: Gross-Pitaevskii equation, splitting step method, Crank-Nicolson algorithm, Numerov algorithm