報告摘要：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.
報告時間：2025年5月12日上午8:30-12:30
報告地點：長沙理工大學云塘校區理科樓A212
報告人簡介：梁慧，哈爾濱工業大學（深圳）理學院副院長、教授、博導。入選首屆“深圳市優秀科技創新人才培養項目（杰出青年基礎研究）”，任期刊《Computational & Applied Mathematics》、《Communications on Analysis and Computation》和《中國理論數學前沿》的編委，中國仿真學會仿真算法專委會委員、中國仿真學會不確定性系統分析與仿真專業委員會秘書、廣東省計算數學學會常務理事、廣東省工業與應用數學學會理事、深圳市數學學會常務理事。主要的研究方向為：延遲微分方程、Volterra積分方程的數值分析。主持國家自然科學基金、深圳市杰出青年基金、深圳市基礎研究計劃等10余項科研項目，獲中國系統仿真學會“優秀論文”獎、黑龍江省數學會優秀青年學術獎、深圳市海外高層次人才。目前已被SCI收錄文章40余篇，發表在SIAM J. Numer. Anal.、IMA J. Numer. Anal.、J. Sci. Comput.、BIT、Adv. Comput. Math.等20余種不同的國際雜志上。