报告题目 (Title)：On the convergence of Galerkin methods for auto-convolution Volterra integral and integro-differential equations
（关于自卷积Volterra积分与积分微分方程的Galerkin方法收敛性分析）
报告人 (Speaker)：梁慧 教授 哈尔滨工业大学（深圳）
报告时间 (Time)：2025年11月20日（周四）10:00
报告地点 (Place)：#腾讯会议：178-839-082
邀请人(Inviter)：李新祥
主办部门：理学院数学系
报告摘要：The auto-convolution Volterra integral and integro-differential equations arise in many applications, for example, in the identification of memory kernels in the theory of viscoelasticity and in the computation of certain special functions. The convergence analysis of piecewise polynomial collocation solutions for these two kinds of equations is now largely well understood. However, the convergence analysis on Galerkin methods is still not clear. In this talk, we will show that the quadrature Galerkin method obtained from the Galerkin method by approximating the inner products by suitable numerical quadrature formulas, is equivalent to the continuous piecewise polynomial collocation method. In addition, the convergence and superconvergence of the numerical solution based on Galerkin methods are investigated.
