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

Abstract: This paper deals with stability properties of Runge–Kutta methods for the initial value problem in nonlinear neutral delay differential equationsThe new concepts of -stability, -stability and Weak -stability are introduced, and it is shown that -algebraically stable Runge–Kutta methods with piecewise linear interpolation are -, - and Weakly -stable. Two numerical examples are given in the end of this paper which confirm our results. [Copyright &y& Elsevier]