Strong convergence of multiscale truncated Euler-Maruyama method for super-linear slow-fast stochastic differential equations

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.