General Modified Split-Step Balanced Methods for Stiff Stochastic Differential Equations

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations （ODEs） solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise.Compared to some other already reported split-step balanced methods,the drift increment function of the methods can be taken from any chosen one-step ordinary differential equations(ODEs)solver.The schemes is proved to be strong convergent with order one.For the mean-square stability analysis,the investigation is confined to two cases.Some numerical experiments are reported to testify the performance and the effectiveness of the methods.