Dissipativity of multistep runge-kutta methods for dynamical systems with delays
Dissipativity of multistep runge-kutta methods for dynamical systems with delays
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DOI：
10.1016/j.mcm.2005.01.019
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发表时间：
2004-12
期刊：
影响因子：
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通讯作者：
Chengming Huang;Q. Chang
中科院分区：
文献类型：
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作者：
Chengming Huang;Q. Chang
本文讨论了用多步Runge-Kutta方法数值求解具有时滞的耗散初值问题。研究了具有约束网格和线性插值过程的（k，l）-代数稳定多步Runge-Kutta方法的耗散性。特别地，证明了代数稳定的、不可约的多步Runge-Kutta方法对有限维时滞动力系统是耗散的，推广和统一了已有的一些结果.此外，利用单支方法与线性多步法之间的关系，我们得到了A-稳定线性多步法的耗散性结果。
This paper is concerned with the numerical solution of dissipative initial value problems with delays by multistep Runge-Kutta methods. We investigate the dissipativity properties of (k, l)-algebraically stable multistep Runge-Kutta methods with constrained grid and linear interpolation procedure. In particular, it is proved that an algebraically stable, irreducible multistep Runge-Kutta method is dissipative for finite-dimensional dynamical systems with delays, which extends and unifies some extant results. In addition, we obtain dissipativity results of A-stable linear multistep methods by using the relationship between one-leg methods and linear multistep methods.