Stability and convergence of arbitrarily high-order multi-product expansion splitting methods for semilinear parabolic problems
数学学科创建110周年系列报告
报告题目(Title)：Stability and convergence of arbitrarily high-order multi-product expansion splitting methods for semilinear parabolic problems
报告人(Speaker)：权超禹（香港中文大学（深圳））
地点(Place)：后主楼1124
时间(Time)：2025年12月26日（周五）17:20-18:00
邀请人(Inviter)：陈华杰
报告摘要
The operator splitting method has been widely used to solve differential equations by splitting the equation into more manageable parts. In this work, we resolve a long-standing problem---how to establish the stability of multi-product expansion (MPE) splitting methods with negative weights. The difficulty occurs because negative weights in high-order MPE method cause the sum of the absolute values of weights larger than one, making standard stability proofs fail. In particular, we take the semilinear parabolic equation as a typical model and establish the stability of arbitrarily high-order MPE splitting methods with positive time steps but possibly negative weights. Rigorous convergence analysis is subsequently obtained from the stability result. Extensive numerical experiments validate the stability and accuracy of various high-order MPE splitting methods, highlighting their efficiency and robustness.
