标题： 隐-显式线性多步法在刚性动力学方程中的应用 显示英文标题

标题： Implicit-explicit linear multistep methods for stiff kinetic equations

摘要： 我们研究了高阶渐近保持线性多步法在动力学方程及其相关问题中的发展。 这些方法首先被开发用于BGK类动力学模型，然后扩展到完整的Boltzmann方程的情形。 还研究了方案在Navier-Stokes极限下的行为，并推导出兼容条件。 我们表明，与IMEX Runge-Kutta方法相比，由于不存在耦合条件且计算效率更高，IMEX多步方案具有多个优势。 后者在处理多维动力学方程的时间离散化时尤为重要。 显示英文摘要

摘要： We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full Boltzmann equation. The behavior of the schemes in the Navier-Stokes regime is also studied and compatibility conditions derived. We show that, compared to IMEX Runge-Kutta methods, the IMEX multistep schemes have several advantages due to the absence of coupling conditions and to the greater computational efficiency. The latter is of paramount importance when dealing with the time discretization of multidimensional kinetic equations.