In recent years, many numerical methods for solving stochastic differential equations have been developed. Some of these methods converge in the weak sense and some others converge in the mean square sense. One of the important features of numerical methods is their stability behavior. In this paper, we focus our attention on stability in expectation (e. stability) of numerical methods of second-order accuracy in the weak sense. The region of e. stability for these methods will be discussed. The possibility of enlarging regions of e. stability will be described. Some numerical examples will be discussed to support the theoretical study.
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