  This paper focuses on explicit approximations for nonlinear stochastic delay
differential equations (SDDEs). Under the weakly local Lipschitz and some
suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs
is proposed, which numerical solutions are bounded and converge to the exact
solutions in qth moment for q>0. Furthermore, the 1/2 order convergent rate is
yielded. Under the Khasminskii-type condition, a more precise TEM scheme is
given, which numerical solutions are exponential stable in mean square and P-1.
Finally, several numerical experiments are carried out to illustrate our
results.
