Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients

A new explicit stochastic scheme of order 1 is proposed for solving commutative differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The method a semi-tamed version Milstein to solve SDEs the drift coefficient consisting non-Lipschitz term and globally term. It easily implementable achieves higher strong convergence order. stability criterion this derived, which shows that condition numerical methods solved keep uniform. Compared some widely used schemes, has better performance in inheriting mean square exact solution SDEs. Numerical experiments are given illustrate obtained properties.