TY - JOUR
T1 - A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations
AU - Shi , Yao
AU - Ma , Qiang
AU - Ding , Xiaohua
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1219
EP - 1247
PY - 2019
DA - 2019/06
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0157
UR - https://global-sci.org/intro/article_detail/aamm/13208.html
KW - Fractional Klein-Gordon-Schrödinger equations, Riesz fractional derivative, conservative scheme, stability, convergence.
AB - <p style="text-align: justify;">In this paper, we study a fourth-order quasi-compact conservative difference scheme for solving the fractional Klein-Gordon-Schrödinger equations. The scheme constructed in this work can preserve exactly the discrete charge and energy conservation laws under Dirichlet boundary conditions. By the energy method, the proposed quasi-compact conservative difference scheme is proved to be unconditionally stable and convergent with order $\mathcal{O}(\tau^{2}+h^{4})$ in maximum norm. Finally, several numerical examples are given to confirm the theoretical results.</p>