Abstract

In this talk, we will present and analyze an energy dissipative time-stepping method for the time fractional gradient flows. The key property of the proposed method is its unconditional stability for general meshes, including the graded mesh commonly used for this type of equations. The unconditional stability is proved through establishing a discrete nonlocal free energy dispassion law. The main idea used in the analysis is to split the time fractional derivative into two parts: a local part and a history part, which are discretized by the well-known L1, L1-CN, $L1^{+}$-CN, and L2 schemes with the sum of exponentials (SOE) technique to reduce the computing storage . Then the scalar auxiliary variable approach is used to deal with the nonlinear and history term. Finally, the efficiency of the proposed method is verified by a series of numerical experiments.