This work focuses on solving super-linear stochastic differential equations (SDEs) involving different time scales numerically. Taking advantages of being explicit and easily implementable, a multiscale truncated Euler-Maruyama scheme is proposed for slow-fast SDEs with local Lipschitz coefficients. By virtue of the averaging principle, the strong convergence of its numerical solutions to the exact ones in pth moment is obtained. Furthermore, under mild conditions on the coefficients, the corresponding strong error estimate is also provided. Finally, two examples and some numerical simulations are given to verify the theoretical results.

翻译：本文聚焦于求解涉及不同时间尺度的超线性随机微分方程的数值方法。利用显式格式易于实现的优点，针对具有局部Lipschitz系数的慢快随机微分方程，提出了一种多尺度截断Euler-Maruyama格式。基于平均化原理，证明了其数值解在p阶矩意义下强收敛于精确解。进一步地，在系数满足温和条件下，给出了相应的强误差估计。最后，通过两个算例及数值模拟验证了理论结果。