Efficient linear energy dissipative difference schemes for the coupled nonlinear damped space fractional wave equations

Abstract

In this paper, several efficient energy dissipative linear difference schemes are presented and analyzed for solving the coupled nonlinear damped fractional wave equations. First, the weighted shifted Grünwald difference formula is used to approach the considered fractional system in space direction. Then, we apply second-order centered difference scheme and invariant energy quadratization Crank-Nicolson scheme to discrete the resulting system in time direction, respectively. Subsequently, the convergence and stability of the proposed schemes are discussed. By using the discrete energy method and a ‘cut-off’ function technique, it is proven that the suggested schemes attain the convergence orders of O(Δt2+h2) in the discrete L2- and L∞- norms, without any time step restrictions dependent on the spatial mesh size. Finally, some numerical results are provided to elucidate the physical behavior and unconditional energy stability of the proposed schemes, and confirm the correctness of theoretical results.