Nonlinear stability of one-leg methods for delay differential equations of neutral type

This paper is devoted to investigations into numerical stability properties of one-leg methods for nonlinear neutral delay differential equations. At first, a series of new stability concepts, such as GS-stability, GAS-stability and Weak GS-stability, are introduced. Then it is proved that a strongly A-stable one-leg method with linear interpolation is GAS-stable, and that an A-stable one-leg method with linear interpolation is GS-stable and Weakly GS-stable. Some numerical experiments are given in the last section of this paper which confirm our results.