Roundoff error problems in interpolation methods for time-fractional problems
数学专题报告
报告题目(Title)：Roundoff error problems in interpolation methods for time-fractional problems
报告人(Speaker)：权超禹（香港中文大学（深圳））
地点(Place)：后主楼1225
时间(Time)：2023年12月4日（周一）15:00-16:00
邀请人(Inviter)：陈华杰
报告摘要
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 $\delta$-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.
