報告人：張啟峰（浙江理工大學）

報告題目：Conservative compact difference schemes for evolution equations with Burgers' type nonlinearity

報告摘要：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.

報告時間：2025年3月1日（星期六）10:00-12:00

報告地點：科技樓706會議室

邀請人：張誠堅

報告人簡介：張啟峰，博士，浙江理工大學副教授。主要研究非線性發展方程的高效保結構算法。曾訪問加拿大、瑞士、新加坡、香港、台灣、澳門等高校，美國《數學評論》和《數學文摘》的評論員。主持完成國家自然科學基金青年基金、博士後基金和浙江省自然科學基金項目，在SIAM J. Sci. Comput., Adv. Comput. Math., J. Sci. Comput., Calcolo, Physics D, JDE等重要數學期刊發表論文60餘篇，并擔任《中國理論數學前沿》雜志編委及30餘個計算與應用數學雜志的審稿人。