An adaptive Euler-Maruyama scheme for McKean SDEs with super-linear growth and application to the mean-field FitzHugh-Nagumo model

Christoph Reisinger, Wolfgang Stockinger

Published 2020-05-12Version 1

In this paper, we introduce a fully implementable, adaptive Euler-Maruyama scheme for McKean SDEs with non-globally Lipschitz continuous drifts. We prove moment stability of the discretised processes and a strong convergence rate of 1/2. We present several numerical examples centred around a mean-field model for FitzHugh-Nagumo neurons, which illustrate that the standard uniform scheme fails and that the adaptive scheme shows in most cases superior performance compared to tamed approximation schemes. In addition, we propose a tamed and an adaptive Milstein scheme for a certain class of McKean SDEs.