✦ LIBER ✦

Nonlinear stability of Runge–Kutta methods for neutral delay differential equations

✍ Scribed by Wan-Sheng Wang; Shou-Fu Li; Kai Su

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 277 KB
Volume: 214
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.02.031

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✦ Synopsis

This paper deals with stability properties of Runge-Kutta methods for the initial value problem in nonlinear neutral delay differential equations

The new concepts of GS(l)-stability, GAS(l)-stability and Weak GAS(l)-stability are introduced, and it is shown that (k, l)algebraically stable Runge-Kutta methods with piecewise linear interpolation are GS(l)-, GAS(l)-and Weakly GAS(l)-stable.

Two numerical examples are given in the end of this paper which confirm our results.

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