Abstract 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 ( Δ t 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.

中文翻译：

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具有阻尼的强耦合非线性空间分数阶波动方程的两种新能量耗散差分格式

摘要 本文首先提出并分析了强耦合非线性阻尼空间分数阶波动方程的两种新的高效耗能差分格式，分别涉及两级非线性差分格式和基于不变量的三级线性差分格式。能量平方公式。然后严格展示了所提出方案的离散能量耗散特性、可解性、无条件收敛性和稳定性。通过离散能量分析方法，刚性地表明所提出的方案在相关数值解的离散L ∞ -范数中实现了O (Δt 2 + h 2 )的无条件收敛率。最后，