A stabilization of multistep linearly implicit schemes for dissipative systems
A stabilization of multistep linearly implicit schemes for dissipative systems
复制标题
耗散系统多步线性隐式方案的稳定性
DOI：
10.1016/j.cam.2013.12.028
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
D. Furihata
中科院分区：
文献类型：
--
作者：
T. Matsuo;D. Furihata
我们考虑耗散梯度系统的数值积分。对于此类系统，已知一类严格维持耗散的特殊、稳定的积分器，但它们通常会产生昂贵的完全隐式方案，并且当系统很大时，线性化对于实际效率是必不可少的。然而，这反过来又会破坏原本预期的稳定性，并且迄今为止还没有制定出稳定线性化的有效原理。在这篇文章中，我们指出线性化方案的行为可以从动力系统理论的角度来理解，并提出了稳定线性化的简单原理。
We consider numerical integration of dissipative gradient systems. For such systems, a class of special, stable integrators that strictly maintain dissipation is known, but they generally yield expensive fully implicit schemes, and when the system is large, linearization is indispensable for practical efficiency. However, this can in turn destroy the originally expected stability, and so far no effective principle has been formulated for a stable linearization. In this note, we point out that the behavior of the linearized schemes can be understood from a dynamical systems theory viewpoint and propose a simple principle for a stable linearization.