题目：Roundoff Error Problems in Interpolation Methods for Time-Fractional Problems

主讲人：权超禹

邀请人：黄巧龙 副研究员

摘要：Roundoff errors often disrupt interpolation methods for time-fractional equations, potentially causing suboptimal convergence or even failure. These issues primarily result from catastrophic cancellations. To address this, we introduce a novel framework for computing coefficients in standard and fast interpolation methods on nonuniform meshes. We propose δ-cancellation and associated threshold conditions to prevent such cancellations. If the thresholds aren't met, a Taylor expansion technique can be applied. Numerical experiments demonstrate our method's accuracy, on par with the Gauss--Kronrod quadrature, but significantly more efficient, allowing for extensive simulations with hundreds of thousands of time steps.

主讲人简介：权超禹，香港中文大学（深圳）助理教授，主要从事隐式溶剂化模型、相场方程高精度数值算法、时间分数阶问题数值方法等方面的研究。2013年本科毕业于中国科学技术大学，2014年硕士毕业于巴黎第九大学，2017年博士毕业于巴黎第六大学Lions实验室，导师为Yvon Maday和Benjamin Stamm教授。

时间：2024年1月17日 下午 14:00-15:00

地点：腾讯会议 848-785-324