Stability and error analysis of one-leg methods for nonlinear delay differential equations

This paper is concerned with the numerical solution of delay differential equations (DDEs). We focus on the stability behaviour and error analysis of one-leg methods with respect to nonlinear DDEs. The new concepts of GR-stability, GAR-stability and weak GAR-stability are introduced. It is proved that a strongly A-stable one-leg method with linear interpolation is GAR-stable, and that an A-stable one-leg method with linear interpolation is GR-stable, weakly GAR-stable and D-convergent of order s, if it is consistent of order s in the classical sense.