Superconvergence of projection integrators for conservative system

主讲人：王雨顺

摘要：Projection method is applicable in many fields. It is a natural and practical approach to construct invariant-preserving schemes for conservative systems by projecting the solution of any underlying numerical scheme onto the manifold determined by the invariant, and this process will be referred as projection integrator. A general result for this projection integrator is that it can achieve the same order accuracy as the underlying method. In this paper, we propose a new projection integrator with superconvergence and further discover that the superconvergence is attributed to the projection direction. This paper also summarizes arbitrarily high-order projection integrators with superconvergence and rigorously proves truncation error by utilizing the linear integral methods as a central tool. Meanwhile, symmetry is significant geometric property in the geometric integration for reversible differential equation, so we also establish arbitrarily high-order symmetric projection integrators with superconvergence and provide the corresponding proof. A thorough comparison with the standard projection integrator is carried out.

主讲人简介：王雨顺，南京师范大学教授、博导。长期从事保结构算法及其应用研究，已经主持7项国家基金委项目，同时作为主要成员参加科技部“863”课题、“973”项目、“863”计划、基金委重点项目，入选江苏省“333”工程、江苏省青蓝工程学术带头人、江苏省“六大人才高峰”高层次人才；江苏省创新团队主持人；获得江苏省科学技术奖，江苏省数学成就奖。专著《偏微分方程保结构算法》获得中国政府图书奖。现任期刊International Journal of Computer Mathematics、《计算数学》编委，江苏省计算数学分会秘书长。

邀请人：李东方

时间：2022年6月23日（星期四）15:00-17:00

地点：腾讯会议室     ID:261627510