Regularity properties of one-leg methods for delay differential equations

The main purpose of this paper is to investigate the asymptotic states of o ne-leg methods for multidelay differential equations. In particular, the ex istence 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 i ntroduced 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. (C) 2001 Elsevier Science Ltd. A ll rights reserved.