Nonlinear stability of general linear methods for neutral delay differential equations

This paper is concerned with the numerical solution of neutral delay differential equations (NDDEs). We focus on the stability of general linear methods with piecewise linear interpolation. The new concepts of GS(p)GS(p)-stability, GAS(p)GAS(p)-stability and weak GAS(p)GAS(p)-stability are introduced. These stability properties for (k,p,0)(k,p,0)-algebraically stable general linear methods (GLMs) are further investigated. Some extant results are unified.