Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping

摘要

In this paper, two new efficient energy dissipative difference schemes for the strongly coupled nonlinear damped space fractional wave equations are first set forth and analyzed, which involve a two-level nonlinear difference scheme, and a three-level linear difference scheme based on invariant energy quadratization formulation. Then the discrete energy dissipation properties, solvability, unconditional convergence and stability of the proposed schemes are exhibited rigidly. By the discrete energy analysis method, it is rigidly shown that the proposed schemes achieve the unconditional convergence rates of O(Δt~2 + h~2) in the discrete L~∞-norm for the associated numerical solutions. At last, some numerical results are provided to illustrate the dynamical behaviors of the damping terms and unconditional energy stability of the suggested schemes, and testify the efficiency of theoretical results.