Time two-grid technique combined with temporal second order difference method for semilinear fractional diffusion-wave equations.

In this paper, we construct two high order difference schemes for semilinear fractional diffusion-wave equations by a symmetric order reduction method and standard order reduction method at first. To improve the computational efficiency, an efficient time two-grid algorithm is then proposed. The global convergence order of the two-grid schemes reaches $ O(\tau_F^2+\tau_C^4+h^2) $, where $ \tau_F $ and $ \tau_C $ represent the time-step sizes on the fine and coarse grids respectively, while $ h $ is the space-step size. Furthermore, stability and convergence analysis of the derived schemes are carefully verified by the energy method. Finally, a numerical experiment is carried out to show the effectiveness of theoretical statements. [ABSTRACT FROM AUTHOR]