@article{Ma2023, 
author = {Tingting Ma and Yayun Fu and Yuehua He and Wenjie Yang},
title = {A linearly implicit energy-preserving exponential time differencing scheme for the fractional nonlinear Schrödinger equation},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {3},
pages = {1105-1117},
keywords = {fractional nonlinear Schrödinger equation, invariant energy quadratization, structure-preserving algorithm, exponential time differencing},
url = {https://www.sciopen.com/article/10.3934/nhm.2023048},
doi = {10.3934/nhm.2023048},
abstract = {In this paper, we present a new method to solve the fractional nonlinear Schrödinger equation. Our approach combines the invariant energy quadratization method with the exponential time differencing method, resulting in a linearly-implicit energy-preserving scheme. To achieve this, we introduce an auxiliary variable to derive an equivalent system with a modified energy conservation law. The proposed scheme uses stabilized exponential time differencing approximations for time integration and Fourier pseudo-spectral discretization in space to obtain a linearly-implicit, fully-discrete scheme. Compared to the original energy-preserving exponential integrator scheme, our approach is more efficient as it does not require nonlinear iterations. Numerical experiments confirm the effectiveness of our scheme in conserving energy and its efficiency in long-time computations.}
}