Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space

This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Hölder-Zygmund space $C^{-\gamma }$ of negative order $-\gamma <0$ in the spatial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong $L^1$ convergence rate. We finally implement the scheme and discuss the results obtained.