报告人：Anatoly Alikhanov（北高加索联邦大学）

邀请人：李东方

报告时间：2023年7月24日（星期一）14:30-17:30

报告地点：科技楼南楼706室

报告题目：A high-order L2 type difference scheme for the time-fractional diffusion equation

报告摘要：The talk is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating approximations of the second and fourth order in space and the (3 − α)th-order in time for the time fractional diffusion equation with variable coefficients. Difference schemes were also constructed for the variable-order diffusion equation and the generalized fractional-order diffusion equation of the Sobolev type. Stability of the schemes under consideration as well as their convergence with the rate equal to the order of the approximation error are proven. The received results are supported by the numerical computations performed for some test problems.

报告人简介：Anatoly Alikhanov，北高加索联邦大学研究员，副校长，数学与计算机中心主任。Anatoly Alikhanov教授主要从事分数阶微分方程数值算法的研究，提出了著名了L2-\sigma格式，主持了多项俄罗斯自然科学基金。