In this paper, we focus on the fast computation for solving the fourth-order time fractional diffusion wave equations with variable coefficient. A fast difference scheme is derived by applying the $\mathcal{FL}2-1_{\sigma }$ formula to approximate the time Caputo fractional derivative. The resulting $\mathcal{FL}2-1_{\sigma }$ scheme keeps the almost same accuracy with the traditional $\mathcal{L}2-1_{\sigma }$ scheme, but it reduces the computational complexity significantly. The solvability, unconditional stability and convergence under the maximum norm of the scheme are proved strictly by using the discrete energy method. Numerical results are given to verify the performance of our scheme.

中文翻译：

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变系数时间分数扩散波方程的快速差分格式

在本文中，我们专注于求解具有可变系数的四阶时间分数阶扩散波方程的快速计算。快速差异方案是通过应用$\mathcal{佛罗里达州}\mathrm{2个}-{\mathrm{1个}}_{\sigma }$近似时间Caputo分数导数的公式。所结果的$\mathcal{佛罗里达州}\mathrm{2个}-{\mathrm{1个}}_{\sigma }$ 方案保持了与传统方法几乎相同的准确性 $\mathcal{大号}\mathrm{2个}-{\mathrm{1个}}_{\sigma }$方案，但是它显着降低了计算复杂度。通过离散能量方法，严格证明了该方案在最大范数下的可解性，无条件稳定性和收敛性。数值结果证明了该方案的性能。