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The truncated Euler-Maruyama (EM) method is proposed to approximate a classof non-autonomous stochastic differential equations (SDEs) with the H\"oldercontinuity in the temporal variable and the super-linear growth in the statevariable. The strong convergence with the convergence rate is proved. Moreover,the strong convergence of the truncated EM method for a class of highlynon-linear time-changed SDEs is studied.

Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations