Before revision:  By rigorous error analysis, we first show that the ELRI scheme provides the first order accuracy in H^\gamma for initial data in H^{\gamma+1} for \gamma>  \frac12 . Moreover, by adding two more correction terms to the first order scheme, we show a second order ELRI that provides the second order accuracy in H^\gamma for initial data in H^{\gamma+3} \ge0 .
After revision:  By rigorous error analysis, we first show that the ELRI scheme provides the first order accuracy in H^\gamma for initial data in H^{\gamma+1} for \gamma>  \frac12 . Moreover, by adding two more correction terms to the first order scheme, we show a second order ELRI that provides the second order accuracy in H^\gamma for initial data in H^{\gamma+3} for \gamma\ge0 .