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.

报告时间：2025年5月12日上午8:30-12:30

报告地点：新利官网开户 云塘校区理科楼A212

报告人简介：梁慧，哈尔滨工业大学（深圳）理学院副院长、教授、博导。入选首届“深圳市优秀科技创新人才培养项目（杰出青年基础研究）”，任期刊《Computational & Applied Mathematics》、《Communications on Analysis and Computation》和《中国理论数学前沿》的编委，中国仿真学会仿真算法专委会委员、中国仿真学会不确定性系统分析与仿真专业委员会秘书、广东省计算数学学会常务理事、广东省工业与应用数学学会理事、深圳市数学学会常务理事。主要的研究方向为：延迟微分方程、Volterra积分方程的数值分析。主持国家自然科学基金、深圳市杰出青年基金、深圳市基础研究计划等10余项科研项目，获中国系统仿真学会“优秀论文”奖、黑龙江省数学会优秀青年学术奖、深圳市海外高层次人才。目前已被SCI收录文章40余篇，发表在SIAM J. Numer. Anal.、IMA J. Numer. Anal.、J. Sci. Comput.、BIT、Adv. Comput. Math.等20余种不同的国际杂志上。