报告人: 陈虎（北京计算科学研究中心）

报告题目: Error analysis of a second-order method on fitted meshes for atime-fractional diffusion problem.

报告摘要：Alikhanov’s high-order scheme for Caputo fractional derivatives of order α ∈ (0, 1) is generalized to nonuniform meshes and analysed for initial-value problems (IVPs) and initial-boundary value problems (IBVPs) whose solutions display a typical weak singularity at the initial time. It is shown that, when the mesh is chosen suitably, the scheme attains order 3 − α convergence for the 1-dimensional IVP and second-order convergence for the IBVP, for which a spectral method is analysed when the spatial domain is the unit square and the extension of this analysis to other spatial domains and other spatial dimensions and discretisations is outlined. Numerical results demonstrate the sharpness of the theoretical convergence estimates.

报告时间: 2019年1月16日（星期三）下午16:00-17:00

报告地点: 科技楼南楼602室