Full implicit schemes for stochastic differential equations with one noise

Two kinds of full implicit numerical schemes for stochastic differential equations in the It o sense are given via construction of the numerical methods for the equivalent stochastic differential equations in the sense of Stratonovich and Backward-It o . This approach could be applied to the stochastic differential equations with one noise, and we prove that the two methods which are generated by the equivalent stochastic differential equations are of mean-square order 1.