Before revision:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order  known for the Lipschitz case cannot be recovered for all presented schemes.
After revision:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order 1/2 known for the Lipschitz case cannot be recovered for all presented schemes.