Arbitrary high-order exponential integrators conservative schemes for the nonlinear Gross-Pitaevskii equation. (1st September 2022)

• Record Type: Journal Article
• Authors: Fu, Yayun; Hu, Dongdong; Zhang, Gengen
• Is Part Of: Computers & mathematics with applications. Volume 121(2022)
• Page Start: 102
• Page End: 114
• Publication Date: 2022-09-01
• Subjects: Gross-Pitaevskii equation -- Exponential integrators -- Scalar auxiliary variable -- Symplectic Runge-Kutta methods -- Conservative schemes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.07.004
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.