The discrete dynamics of nonlinear infinite-delay-differential equations

Abstract This paper deals with numerical stability of nonlinear infinite-delay systems of the form y′(t) = ƒ(t,y(t),y(pt)) (p ∈ (0, 1), t > 0) . Recently, linear stability properties of some numerical methods for infinite delay systems have been studied by several authors (cf. [1–9]). However, few results have been devoted to the nonlinear case. This paper considers global and asymptotic stability of one-leg θ-methods for the above nonlinear systems. Some stability criteria are obtained.

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