Affiliation:
1. Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King's College Road Toronto M5R 0A3 Ontario Canada
2. College of Science and Engineering James Cook University Townsville QLD 4811 Australia
3. Lassonde School of Engineering York University Toronto M3J 1P3 Ontario Canada
Abstract
Herein, an efficient numerical solver for stochastic differential equations based on memristors is presented. The solver utilizes the stochastic switching effect in memristive devices to simulate the generation of a Brownian path and employs iterative Euler method computations within memristive crossbars. The correctness of the solution paths generated by the system is examined by solving the Black–Scholes equations and comparing the paths to analytical solutions. It is found that the absolute error of a 128‐step path is limited to an order of . The tolerance of the system to crossbar nonidealities is also assessed by comparing the numerical and analytical paths' variation in error. The numerical solver is sensitive to the variation in operating conditions, with the error increasing by , , and as the ambient temperature, wire resistance, and stuck probability of the memristor increase to extreme conditions. The solver is tested on a variety of problems to show its utility for different calculations. And, the resource consumption of the proposed structure built with existing technology is estimated and it is compared with similar iterative solvers. The solver generates a solution with the same level of accuracy from to faster than similar digital or mixed‐signal designs.
Funder
Natural Sciences and Engineering Research Council of Canada
Cited by
1 articles.
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