Exponential multistep methods of Adams-type
Exponential multistep methods of Adams-type
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DOI：
10.1007/s10543-011-0332-6
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发表时间：
2011-12-01
影响因子：
1.5
通讯作者：
Ostermann, Alexander
中科院分区：
文献类型：
--
作者：
Hochbruck, Marlis;Ostermann, Alexander
本文研究指数多步法的构造、实现和数值分析。这些方法与显式亚当斯方法有关，但与后者相反，直接使用指数和相关的矩阵函数的（可能粗糙）线性化的向量场。这一特性使他们能够在时间上显式地积分刚性问题。在包含半线性发展方程及其空间离散的线性半群的抽象框架中进行刚性误差分析。所提出的方法，包括初始值的计算和Krylov子空间方法的产生矩阵函数的评估的一种可能的实现进行了讨论。此外，建立了指数型亚当斯方法与一类局部时间推进格式之间的有趣联系，并给出了数值例子来说明方法的性质。
The paper is concerned with the construction, implementation and numerical analysis of exponential multistep methods. These methods are related to explicit Adams methods but, in contrast to the latter, make direct use of the exponential and related matrix functions of a (possibly rough) linearization of the vector field. This feature enables them to integrate stiff problems explicitly in time.A stiff error analysis is performed in an abstract framework of linear semigroups that includes semilinear evolution equations and their spatial discretizations. A possible implementation of the proposed methods, including the computation of starting values and the evaluation of the arising matrix functions by Krylov subspace methods is discussed. Moreover, an interesting connection between exponential Adams methods and a class of local time stepping schemes is established.Numerical examples that illustrate the methods' properties are included.