期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 121, 期 -, 页码 102-114出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2022.07.004
关键词
Gross-Pitaevskii equation; Exponential integrators; Scalar auxiliary variable; Symplectic Runge-Kutta methods; Conservative schemes
资金
- National Natural Science Foundation of China [11701110]
- National Natural Science Foundation of Henan Province [222300420280]
- Program for Scientific and Technological Innovation Talents in Universities of Henan Province [22HASTIT018]
- National Natural Science Cultivation Foundation of Xuchang University [2022GJPY003]
- Innovation team of School of Mathematics and Statistics, Yunnan University [ST20210104]
This paper proposes a family of high-order conservative schemes based on the exponential integrators technique and the symplectic Runge-Kutta method for solving the nonlinear Gross-Pitaevskii equation. Numerical examples are provided to confirm the accuracy and conservation of the developed schemes.
In this paper, we propose a family of high-order conservative schemes based on the exponential integrators technique and the symplectic Runge-Kutta method for solving the nonlinear Gross-Pitaevskii equation. By introducing generalized scalar auxiliary variable, the equation is equivalent to a new system with both mass and modified energy conservation laws. Then, a conservative semi-discrete exponential scheme is given by combining the symplectic Runge-Kutta method and the Lawson method in the time direction. Subsequently, we apply the Fourier pseudo-spectral method to approximate semi-discrete system in space and obtain the fully -discrete schemes that conserve the energy and mass. Numerical examples are presented to confirm the accuracy and conservation of the developed schemes.
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