Techniques for reliable and accurate numerical solutions of memristor models

This work presents techniques for an accurate numerical simulation of memristor models. In physics-based models of extended memristors under indirect excitation, the solution of the state equations is constrained to lie on specific manifolds at all times. A possible algorithm for the determination of numerical solutions to the algebraic differential equation set typical of these systems consists of augmenting the state vector with a novel variable which is invariant on the manifold. Solving the resulting ordinary differential equation problem simplifies the simulation since the algebraic constraint is embedded into the state equations. Regarding mathematical descriptions of generic memristors, where the state may only lie within a closed set, a procedure identifying each undesired event where the state either exceeds the upper bound or goes below the lower one, stopping the current simulation, starting a new one with initial condition set to the violated limit, and finally concatenating the time series of the various simulation sections, ensures a well-behaved simulation run, and, consequently, a reliable numerical solution. Examples from a number of case studies demonstrate that the adoption of the proposed techniques prevents possible issues emerging in classical numerical integration methodologies, resulting in well-behaved state solutions, thus allowing a meaningful exploration of the full potential of memristors in electronic circuit design.