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Motivated by truncated EM method introduced by Mao (2015), a new explicitnumerical method named modified truncated Euler-Maruyama method is developed inthis paper. Strong convergence rates of the given numerical scheme to the exactsolutions to stochastic differential equations are investigated under givenconditions in this paper. Compared with truncated EM method, the givennumerical 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 areprovided to support our conclusions.

Strong convergence rates of modified truncated EM method for stochastic differential equations