arXiv:2512.15141v4 Announce Type: replace Abstract: In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we investigate the uniqueness, stability, and convergence of the scheme. Furthermore, we prove that the scheme achieves second-order convergence in both time and space. Finally, corresponding numerical examples are provided.