报告题目：Introduction of the theory of difference equations

主 讲 人：Timur K. Iskakov副教授（俄罗斯新西伯利亚国立大学, Sobolev数学研究所）

报告邀请人：李树光 副教授

报 告 时间：2025年09月16日下午13:30-15:30

报告地点：数理楼 224

报告摘要：The course of lectures is devoted to the theory of difference equations. Such equations arise in the modeling of various processes in natural science, in the numerical solving of differential equations, etc. Some models will be presented in the first lecture. The basic properties of linear systems of difference equations will be considered. Further lectures will be devoted to the theory of stability. For linear systems of difference equations, several conditions of stability will be formulated and proved. In the second lecture, spectral conditions of stability will be described, which are difficult to verify in practice. In the third lecture, the stability conditions will be considered in terms of the solvability of the discrete Lyapunov matrix equation. Estimates of solutions to a linear autonomous system of difference equations will be established using solutions to the matrix equation. The fourth lecture will address the problem of stability of solutions under the perturbations of coefficients and the problem of stability of solutions to nonlinear systems.

个人简历：Timur K. Iskakov是新西伯利亚国立大学副教授；俄罗斯科学院Sobolev数学研究所高级研究员，物理数学科学副博士。研究领域包括偏微分方程、差分方程和计算线性代数。发表了20多篇高水平文章。