Unconditional Energy Dissipation and Error Estimates of the SAV Fourier Spectral Method for Nonlinear Fractional Generalized Wave Equation

In this paper, we consider a second-order scalar auxiliary variable Fourier spectral method to solve the nonlinear fractional generalized wave equation. Unconditional energy conservation or dissipation properties of the fully discrete scheme are first established. Next, we utilize the temporal-spatial error splitting argument to obtain unconditional optimal error estimate of the fully discrete scheme, which overcomes time-step restrictions caused by strongly nonlinear system, or the restrictions that the nonlinear term needs to satisfy the assumption of global Lipschitz condition in all previous works for fractional undamped or damped wave equations. Finally, some numerical experiments are presented to confirm our theoretical analysis.