报告题目：Collocation methods for integral-algebraic equations and integro-differential algebraic equaitons
报 告 人：梁慧教授
工作单位：哈尔滨工业大学（深圳）
报告时间：2021-11-26(周五) 15:30-17:30
腾讯会议ID：480 107 504
报告摘要：
Our analysis of collocation solutions for general systems of linear integral-algebraic equations (IAEs) is based on the notions of the tractability index and the smoothing property of a Volterraintegral operator. These are used to decouple the given IAE system into the inherent system of regular second-kind Volterraintegral equations (VIEs) and a system of first-kind VIEs. This decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions for index-1 IAEs. The notion of the tractability index and decoupling is extended to integro-differential algebraic equations (IDAEs). The convergence of collocation methods is established for index-1 IDAEs.
报告人简介：
梁慧，哈尔滨工业大学（深圳）理学院教授。2008年博士毕业于哈尔滨工业大学，曾多次访问香港浸会大学，2017-2018年在加拿大纽芬兰纪念大学做访问学者。主要研究兴趣为延迟微分方程以及Volterra积分方程数值方法。主持国家自然科学基金、青年基金、黑龙江省普通本科高等学校青年创新人才培养计划等10余项科研项目。在计算数学领域著名期刊SIAM J. Numer. Anal., IMA J. Numer. Anal., BIT等上发表论文三十余篇。
