(untitled) (Advances in Applied Mathematics and Mechanics, 2019)
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 O(τ^2+h^4) in maximum norm. Finally, several numerical examples are given to confirm the theoretical results.