An efficient time-splitting compact finite difference method for Gross–Pitaevskii equation

2017 ◽  
Vol 297 ◽  
pp. 131-144 ◽  
Author(s):  
Hanquan Wang ◽  
Xiu Ma ◽  
Junliang Lu ◽  
Wen Gao
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Pitaevskii Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method ◽  
Time Splitting

scholarly journals An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rongpei Zhang ◽  
Jia Liu ◽  
Guozhong Zhao
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Gradient Flow ◽  
Pitaevskii Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method ◽  
Representation Technique

We present an efficient, unconditionally stable, and accurate numerical method for the solution of the Gross-Pitaevskii equation. We begin with an introduction on the gradient flow with discrete normalization (GFDN) for computing stationary states of a nonconvex minimization problem. Then we present a new numerical method, CFDM-AIF method, which combines compact finite difference method (CFDM) in space and array-representation integration factor (AIF) method in time. The key features of our methods are as follows: (i) the fourth-order accuracy in space andrth (r≥2) accuracy in time which can be achieved and (ii) the significant reduction of storage and CPU cost because of array-representation technique for efficient handling of exponential matrices. The CFDM-AIF method is implemented to investigate the ground and first excited state solutions of the Gross-Pitaevskii equation in two-dimensional (2D) and three-dimensional (3D) Bose-Einstein condensates (BECs). Numerical results are presented to demonstrate the validity, accuracy, and efficiency of the CFDM-AIF method.

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