Abstract
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.
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