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 the spatial variable, in particular being a 1/2-H"older continuous function of time taking values in a H"older-Zygmund space $\mathcal C^{-\gamma}$ of negative order $-\gamma<0$. 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.