Before revision:  With the aid of the previously obtained error bounds, we reveal a mean-square convergence rate of order one for the positivity preserving schemes  under more relaxed conditions, compared with existing relevant results  in the literature.
After revision:  With the aid of the previously obtained error bounds, we reveal a mean-square convergence rate of order one for the positivity preserving schemes for the first time under more relaxed conditions, compared with existing relevant results in the literature.