Numerical solution of isospectral flows
Numerical solution of isospectral flows
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DOI：
10.1090/s0025-5718-97-00902-2
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发表时间：
1997-10
期刊：
影响因子：
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通讯作者：
M. Calvo;A. Iserles;A. Zanna
中科院分区：
文献类型：
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作者：
M. Calvo;A. Iserles;A. Zanna
本文研究等谱流的数值求解问题。这些流由微分方程L' = [B（L），L]; L（0）= L0表征，其中L0是d × d对称矩阵，B（L）是L的反对称矩阵函数，[B，L]是李括号算子.我们表明，标准的龙格-库塔计划未能恢复这些流量的主要定性特征，即isospectrality，因为他们不能恢复任意立方守恒律。这一失败促使我们引入一种替代方法，并建立一个框架，生成任意高阶的等谱方法。
In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation L' = [B(L), L]; L(0) = L 0 , where L 0 is a d x d symmetric matrix, B(L) is a skew-symmetric matrix function of L and [B, L] is the Lie bracket operator. We show that standard Runge-Kutta schemes fail in recovering the main qualitative feature of these flows, that is isospectrality, since they cannot recover arbitrary cubic conservation laws. This failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order.