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- Title
Linearly Implicit High-Order Exponential Integrators Conservative Runge–Kutta Schemes for the Fractional Schrödinger Equation.
- Authors
Fu, Yayun; Zheng, Qianqian; Zhao, Yanmin; Xu, Zhuangzhi
- Abstract
In this paper, a family of high-order linearly implicit exponential integrators conservative schemes is constructed for solving the multi-dimensional nonlinear fractional Schrödinger equation. By virtue of the Lawson transformation and the generalized scalar auxiliary variable approach, the equation is first reformulated to an exponential equivalent system with a modified energy. Then, we construct a semi-discrete conservative scheme by using the Fourier pseudo-spectral method to discretize the exponential system in space direction. After that, linearly implicit energy-preserving schemes which have high accuracy are given by applying the Runge–Kutta method to approximate the semi-discrete system in temporal direction and using the extrapolation method to the nonlinear term. As expected, the constructed schemes can preserve the energy exactly and implement efficiently with a large time step. Numerical examples confirm the constructed schemes have high accuracy, energy-preserving, and effectiveness in long-time simulation.
- Subjects
NONLINEAR Schrodinger equation; SEPARATION of variables; RUNGE-Kutta formulas; INTEGRATORS; SCHRODINGER equation
- Publication
Fractal & Fractional, 2022, Vol 6, Issue 5, p243
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract6050243