报告题目：On applying general algebra to semi-automatic linearization of systems of nonlinear PDEs

主 讲 人：Timofey A. Lomonosov副教授（俄罗斯国立高等经济大学）

报告邀请人：李树光 副教授

报 告 时间：2025年05月06日下午15:30-17:00

报告地点：数理楼 224

报告摘要：We study a three-level explicit in time higher-order vector compact scheme, with additional n sought functions approximating second order non-mixed spatial derivatives of the solution, for an initial-boundary value problem for the n-dimensional wave equation and acoustic wave equation, with the variable speed of sound, n⩾1. We also approximate the solution at the first time level in a similar two-level manner, without using derivatives of the initial data as usual. For the first time, under the CFL-type conditions, new stability bounds in the standard and stronger mesh energy norms and the discrete energy conservation laws are presented, and the corresponding error bounds of the orders 4 and 3.5 are rigorously proved. Generalizations to the cases of the nonuniform meshes in space and time are described. Results of various numerical experiments are also included.

个人简历：Timofey A. Lomonosov是俄罗斯高等经济大学副教授，物理数学科学副博士，毕业于俄罗斯高等经济大学。历任俄罗斯高等经济大学助教、讲师、副教授、高级研究员等。Timofey A. Lomonosov副教授主要从事计算数学和偏微分方程数值解领域的研究，特别是对双曲型方程和可压缩纳维-斯托克斯方程，提出了一系列行之有效的数值计算方法。目前，已发表了40余篇高水平学术文章。