Stability analysis of Runge-Kutta methods for nonlinear delay differential equations (Q1293247)

The new concepts of GR\((l)\)-stability, GAR\((l)\)-stability and weak GAR\((l)\)-stability are introduced to study the stability behaviour of Runge-Kutta methods for nonlinear delay-differential equations. These stability properties are studied for \((k,l)\)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpretation procedure. The stability analysis presented here is closely related to that for nonlinear stiff ordinary differential equations.