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

摘要

This paper deals with stability properties of Runge–Kutta methods for the initial value problem in nonlinear neutral delay differential equationsy′(t)=f(t,y(t),y(t-τ),y′(t-τ)),t⩾0,y(t)=φ(t),t∈[-τ,0].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.