Uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for linear hyperbolic relaxation systems

Abstract

This work is concerned with the uniform accuracy of implicit-explicit backward differentiation formulas for general linear hyperbolic relaxation systems satisfying the structural stability condition proposed previously by the third author. We prove the uniform stability and accuracy of a class of IMEX-BDF schemes discretized spatially by a Fourier spectral method. The result reveals that the accuracy of the fully discretized schemes is independent of the relaxation time in all regimes. It is verified by numerical experiments on several applications to traffic flows, rarefied gas dynamics and kinetic theory.

Speaker Intro

Zhiting Ma obtained the B.S. degree from Lanzhou University in 2015 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University, China in 2021. Currently, she is an Assistant Professor in Beijing Institute of Mathematical Sciences and Applications (BIMSA). Her current research interests include kinetic theory, machine learning and hyperbolic relaxation systems.