应用数学青年讨论班（午餐会）—— 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.

Brief bio:

Zhiting Ma obtained the B.S. degree from Lanzhou University in 2015 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University in 2021. Then, she worked as a postdoc at School of Mathematical Sciences, Peking University. Currently, she is an Assistant Professor in Beijing Institute of Mathematical Sciences and Applications (BIMSA).

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