Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations
Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations
复制标题
DOI：
10.1016/j.apm.2008.10.038
复制
发表时间：
2009-08
影响因子：
5
通讯作者：
Wansheng Wang;Y. Zhang;Shoufu Li
中科院分区：
文献类型：
--
作者：
Wansheng Wang;Y. Zhang;Shoufu Li
利用连续Runge-Kutta方法，给出了非线性中立型时滞微分方程y′（t）=f（t，y（t），y（t-τ（t）），y′（t-τ（t）））（t <$t0）的某些稳定性的正确模拟结果.特别是，它表明，某些连续的龙格-库塔方法的基础上向后欧拉方法或2-阶段Lobatto IIIC方法，结合线性插值，是GRN稳定和渐近稳定的NDEs。
This paper provides results on the correct simulation, when using continuous Runge–Kutta methods, of certain stability properties of nonlinear neutral delay-differential equations (NDDEs) y′(t)=f(t,y(t),y(t-τ(t)),y′(t-τ(t)))(t⩾t0). In particular, it is shown that certain continuous Runge–Kutta methods based upon the backward Euler method or the 2-stage Lobatto IIIC method, combined with linear interpolation, are GRN-stable and asymptotically stable for NDDEs.