@article{Wang2023, 
author = {Junjie Wang and Yaping Zhang and Liangliang Zhai},
title = {Structure-preserving scheme for one dimension and two dimension fractional KGS equations},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {1},
pages = {463-493},
keywords = {Fractional Klein-Gordon-Schrödinger equations, conservation law, convergence, high central difference scheme, scalar auxiliary variable scheme},
url = {https://www.sciopen.com/article/10.3934/nhm.2023019},
doi = {10.3934/nhm.2023019},
abstract = {In the paper, we study structure-preserving scheme to solve general fractional Klein-Gordon-Schrödinger equations, including one dimension case and two dimension case. First, the high central difference scheme and Crank-Nicolson scheme are used to one dimension fractional Klein-Gordon-Schrödinger equations. We show that the arising scheme is uniquely solvable, and approximate solutions converge to the exact solution at the rate    O  (      τ    2    +      h    4    ). Moreover, we prove that the resulting scheme can preserve the mass and energy conservation laws. Second, we show Crank-Nicolson scheme for two dimension fractional Klein-Gordon-Schrödinger equations, and the proposed scheme preserves the mass and energy conservation laws in discrete formulations. However, the obtained discrete system is nonlinear system. Then, we show a equivalent form of fractional Klein-Gordon-Schrödinger equations by introducing some new auxiliary variables. The new system is discretized by the high central difference scheme and scalar auxiliary variable scheme, and a linear discrete system is obtained, which can preserve the energy conservation law. Finally, the numerical experiments including one dimension and two dimension fractional Klein-Gordon-Schrödinger systems are given to verify the correctness of theoretical results.}
}