  Motivated by truncated EM method introduced by Mao (2015), a new explicit
numerical method named modified truncated Euler-Maruyama method is developed in
this paper. Strong convergence rates of the given numerical scheme to the exact
solutions to stochastic differential equations are investigated under given
conditions in this paper. Compared with truncated EM method, the given
numerical simulation strongly converges to the exact solution at fixed time $T$
and over a time interval $[0,T]$ under weaker sufficient conditions. Meanwhile,
the convergence rates are also obtained for both cases. Two examples are
provided to support our conclusions.
