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- W1489503413 abstract "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 and r th (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>r</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math>) 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." @default.
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- W1489503413 date "2015-01-01" @default.
- W1489503413 modified "2023-10-14" @default.
- W1489503413 title "An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation" @default.
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- W1489503413 doi "https://doi.org/10.1155/2015/127580" @default.
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