报告人：张启峰（浙江理工大学）

报告题目：Conservative compact difference schemes for evolution equations with Burgers' type nonlinearity

报告摘要：A novel fourth-order three-point compact operator for the nonlinear convection term is provided. The operator makes the numerical analysis of higher-order difference schemes become possible for a wide class of nonlinear evolutionary equations under the unified framework. We take the classical viscous Burgers' equation as an example and establish a new conservative fourth-order implicit compact difference scheme based on the method of order reduction. A detailed theoretical analysis is carried out by the discrete energy argument and mathematical induction. It is rigorously proved that the difference scheme is conservative, uniquely solvable, stable, and unconditionally convergent in infinite norm. The convergence order is two in time and four in space, respectively. Furthermore, we derive a three-level linearized compact difference scheme for viscous Burgers' equation based on the proposed operator. All numerically theoretical results similar to that of the nonlinear numerical scheme are inherited completely; meanwhile, it is more time saving. Applying the compact operator to other more complex and higher-order nonlinear evolutionary equations is feasible, including BBMB equation, KdV equation, R2CH system and so on.

报告时间：2025年3月1日（星期六）10:00-12:00

报告地点：科技楼706会议室

邀请人：张诚坚

报告人简介：张启峰，博士，浙江理工大学副教授。主要研究非线性发展方程的高效保结构算法。曾访问加拿大、瑞士、新加坡、香港、台湾、澳门等高校，美国《数学评论》和《数学文摘》的评论员。主持完成国家自然科学基金青年基金、博士后基金和浙江省自然科学基金项目，在SIAM J. Sci. Comput., Adv. Comput. Math., J. Sci. Comput., Calcolo, Physics D, JDE等重要数学期刊发表论文60余篇，并担任《中国理论数学前沿》杂志编委及30余个计算与应用数学杂志的审稿人。