Exponential-Krylov methods for ordinary differential equations
Exponential-Krylov methods for ordinary differential equations
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常微分方程的指数-Krylov 方法
DOI：
10.1016/j.jcp.2014.08.013
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Adrian Sandu
中科院分区：
文献类型：
--
作者：
P. Tranquilli;Adrian Sandu
本文提出了一种新的指数时间离散化方法，称为指数Krylov（expK）。新方案将时间离散化和基于Krylov的指数矩阵-向量乘积近似作为一个单一的计算过程。经典的顺序条件理论在这里开发的时间和Krylov近似误差帐户。与传统的指数方案不同，expK方法在每个时间步只需要构造一个Krylov空间。保证时间精度顺序的基向量的数量不取决于手头的应用。数值结果表明，与现有的指数格式相比，expK方法具有良好的性能.
This paper develops a new family of exponential time discretization methods called exponential-Krylov (expK). The new schemes treat the time discretization and the Krylov-based approximation of exponential matrix–vector products as a single computational process. The classical order conditions theory developed herein accounts for both the temporal and the Krylov approximation errors. Unlike traditional exponential schemes,expKmethods require the construction of only a single Krylov space at each timestep. The number of basis vectors that guarantee the temporal order of accuracy does not depend on the application at hand. Numerical results show favorable properties ofexpKmethods when compared to current exponential schemes.