Speaker: Quan Chaoyu, Assistant Professor, the Chinese University of Hong Kong, Shenzhen

Date: January 17, 2024

Time: 14:00-15:00

Location: Tencent Meeting

Sponsor: School of Mathematics, Shandong University

Abstract:

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.

For more information, please visit:

http://www.math.sdu.edu.cn/info/1020/19506.htm