Regularity properties of one-leg methods for delay differential equations

The main purpose of this paper is to investigate the asymptotic states of one-leg methods for multidelay differential equations. In particular, the existence of spurious steady solutions and period-2 solutions in constant or variable timestep is studied, and the concepts of R[1]-regularity and R[2]-regularity of one-leg methods for multidelay differential equations are introduced and studied. Some conditions guaranteeing R[1]-regularity and R[2]-regularity of such methods applied to multidelay differential equations with some important structures are given.