  A large number of simulation models have been proposed over the years to
mimic the electrical behaviour of memristive devices. The models are based
either on sophisticated mathematical formulations that do not account for
physical and chemical processes responsible for the actual switching dynamics
or on multi-physical spatially resolved approaches that include the inherent
stochastic behaviour of real-world memristive devices but are computationally
very expensive. In contrast to the available models, we present a
computationally inexpensive and robust spatially 1D model for simulating
interface-type memristive devices. The model efficiently incorporates the
stochastic behaviour observed in experiments and can be easily transferred to
circuit simulation frameworks. The ion transport, responsible for the resistive
switching behaviour, is modelled using the kinetic Cloud-In-a-Cell scheme. The
calculated current-voltage characteristics obtained using the proposed model
show excellent agreement with the experimental findings.
