Abstract
In this paper, we are concerned with the analytical and numerical stability of nonlinear neutral delay integro-differential equations (NDIDEs). First, sufficient conditions for the analytical stability of nonlinear NDIDEs with a variable delay are derived. Then, we show that any A-stable linear multistep method can preserve the asymptotic stability of the analytical solution for nonlinear NDIDEs with a constant delay. At last, we validate our conclusions by numerical experiments.
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