Given the complexity of the mathematical descriptions of real nanodevices with memristor fingerprints, convergence issues often emerge in the simulation of circuits employing memristors, even for a limited number of instances. Actually the simulation of one-memristor circuits may also be troublesome for some inputs and/or initial conditions. This problem prevents a thorough test of memristor circuit designs, representing a severe obstacle towards an extensive use of memristors in electronics. In this work we propose techniques to transform a highlyreliable physics-based model of the Tantalum oxide memristor from Hewlett Packard Labs in a form which lends itself naturally to stable numerical simulations. The results of this study shall pave the way towards a more extensive exploration of the full potential of memristors in integrated circuit design