The Finite Difference Method for Dissipative Klein-Gordon-Schrödinger Equations in Three Space Dimensions (Journal of Computational Mathematics, 2021)
A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrödinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding theorems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in $H^2× H^2× H^1$ over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
Keywords: Dissipative Klein–Gordon–Schrödinger equations; Finite difference method; Error bounds; Maximal attractor.