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The paper introduces a set of models of memristive devices for a reliable, accurate and fast analysis of large networks in the SPICE (Simulation Program with Integrated Circuit Emphasis) environment. The modeling starts from the recently introduced TEAM (ThrEshold Adaptive Memristor Model) and VTEAM (Voltage ThrEshold Adaptive Memristor Model). A number of improvements are made towards the stick effect elimination and other numerical renements to make the analysis of large networks fast and accurate. A set of models are proposed that utilize the synergy of several techniques such as window asymmetrization, integration with saturation, state equation preprocessing, scaling, and smoothing. The performance of models is tested in Cadence PSPICE 17.2 and particularly in HSPICE v2017, the latter on a large-scale CNN (Cellular Nonlinear Network) for detecting edges of binary images. The simulations manifest the usability of developed models for fast and reliable operation in networks containing more than one million nodes.