论文标题
隐式的收敛结果 - 说明通用线性方法
Convergence Results for Implicit--Explicit General Linear Methods
论文作者
论文摘要
本文研究了隐式阐释的一般线性方法的固定步骤收敛。我们专注于内部一致，具有高阶段顺序和有利稳定性的方案子类。给出了经典的，索引-1差异代数方程和奇异扰动收敛分析结果。对于所有这些问题，兴趣类别的IMEX GLM与一般假设下的完整理论秩序融合在一起。收敛结果要求时间步长足够小，上限与问题的刚度无关。
This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1 differential algebraic equation, and singular perturbation convergence analyses results are given. For all these problems IMEX GLMs from the class of interest converge with the full theoretical orders under general assumptions. The convergence results require the time steps to be sufficiently small, with upper bounds that are independent on the stiffness of the problem.
