Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium No. 131  

Lecture Title: Efficient High Order Semi-Implicit Spectral Deferred Correction Time Discretization

Speaker: Xu Yan (Professor, University of Science and Technology of China)  

Date & Time: 4:30–5:30 PM, May 15, 2025  

Venue: Classroom 1, Huixing Building, Yuehai Campus, Shenzhen University  

Abstract: In this talk, we will present high order spectral deferred correction time discretization methods. We introduce L-stable spectral deferred correction methods with low stages, initiated by the Crank-Nicolson method. By employing a linear stabilization approach for phase field models, we derive a linear implicit SDC scheme. This involves adding and subtracting linear stabilization operators tailored for various phase field problems. We also incorporate an extrapolation technique in the prediction step of the semi-implicit SDC method without compromising the low-stage property. We also adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Furthermore, we construct high-order stabilization terms for semi-implicit deferred correction methods, focusing on convection-diffusion-reaction problems. We investigate optimal choices for stability parameters and analyze the upper bound of the time step to ensure both stability and high-order accuracy. Utilizing Fourier analysis, we apply von Neumann stability and Schur theory to the proposed single-step and multi-step deferred correction methods. Numerical experiments validate the analysis of the stability parameter bounds and time step constraints for these methods.

Biography: Xu Yan is a professor in the School of Mathematical Sciences at the University of Science and Technology of China. She received her Ph.D. in Computational Mathematics from the University of Science and Technology of China in 2005, followed by postdoctoral research at the University of Twente, the Netherlands (2005–2007). In 2009, she was supported by the Humboldt Foundation for a visiting fellowship at the University of Freiburg, Germany. Her research focuses on high-precision numerical methods. Awards include the National Excellent Doctoral Dissertation Award (2008), the NSFC Outstanding Young Scholars Award (2017), and the Second "Youth Innovation Award" from the Computational Mathematics Society of China (2017). She is a member of the Ministry of Education’s "New Century Excellent Talents" program and has led projects such as NSFC General Projects, Humboldt Research Group Linkage Programs, and Fok Ying Tung Young Teachers’ Foundation projects. She serves as a council member of the Computational Mathematics Society of China and an editorial board member for journals including SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, and Communication on Applied Mathematics and Computation and Computational Physics.  

All faculty and students are welcome to attend!

School of Mathematical Sciences

May 13, 2025