Numerical approximation of characteristic values of partial retarded functional differential equations
Numerical approximation of characteristic values of partial retarded functional differential equations
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DOI：
10.1007/s00211-009-0233-7
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发表时间：
2009-08-01
影响因子：
2.1
通讯作者：
Vermiglio, R.
中科院分区：
文献类型：
--
作者：
Breda, D.;Maset, S.;Vermiglio, R.
动态系统平衡点的稳定性由平衡点周围所谓的线性化特征值在复平面中的位置决定。本文提出了一种基于伪谱法与谱法相结合的时滞演化偏微分方程特征值的计算方法。所计算的特征值的收敛对于伪谱离散化而言是无限阶的，而对于谱离散化而言是有限阶的。然而，对于一维反应扩散方程，谱离散化的有限阶被证明是如此之高，以至于收敛速度与无限阶之一一样快。
The stability of an equilibrium point of a dynamical system is determined by the position in the complex plane of the so-called characteristic values of the linearization around the equilibrium. This paper presents an approach for the computation of characteristic values of partial differential equations of evolution involving time delay, which is based on a pseudospectral method coupled with a spectral method. The convergence of the computed characteristic values is of infinite order with respect to the pseudospectral discretization and of finite order with respect to the spectral one. However, for one dimensional reaction diffusion equations, the finite order of the spectral discretization is proved to be so high that the convergence turns out to be as fast as one of infinite order.