报告人：Anatoly A. Alikhanov（北高加索联邦大学）

邀请人：李东方

报告时间：2023年11月18日（星期六）9:00-12:00

报告地点：Zoom: 856 227 780 71

报告题目：A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay

报告摘要：This talk considers a class of the time-fractional diffusion-wave equation (TFDWE), which incorporates a fractional derivative in the Caputo sense. Initially, the original problem is transformed into a new model that incorporates the fractional Riemann–Liouville integral. Subsequently, a more generalized model is considered and investigated, which includes the generalized fractional integral with memory kernel. The paper establishes the existence and uniqueness of a numerical solution for the problem. We introduce a discretization technique for approximating the generalized fractional Riemann–Liouville integral and study its fundamental properties. Based on this technique, we propose a second-order numerical scheme for approximating the generalized model. The proof of the stability of the proposed difference scheme when considered in terms of the L2 norm is established. Furthermore, a difference scheme is devised for solving a nonlinear generalized model with time delay. The convergence and stability analysis of this particular case are established using the discrete Gronwall inequality. Numerical examples are provided to evaluate the effectiveness and reliability of the proposed methods and to support our theoretical analysis

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。