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.

翻译：本文研究满足第三作者先前提出的结构稳定性条件的一般线性双曲松弛系统的隐式-显式向后微分公式的一致精度。我们证明了采用傅里叶谱方法进行空间离散的一类IMEX-BDF格式的一致稳定性和精度。结果表明，全离散格式的精度在所有区域均与松弛时间无关。该结论通过交通流、稀薄气体动力学和动理学理论等多个应用领域的数值实验得到验证。