  Over the last few decades, the numerical methods for stochastic differential
delay equations (SDDEs) have been investigated and developed by many scholars.
Nevertheless, there is still little work to be completed. By virtue of the
novel technique, this paper focuses on the mean-square convergence and
stability of the backward Euler method (BEM) for SDDEs whose drift and
diffusion coefficients can both grow polynomially. The upper mean-square error
bounds of BEM are obtained. Then the convergence rate, which is one-half, is
revealed without using the moment boundedness of numerical solutions.
Furthermore, under fairly general conditions, the novel technique is applied to
prove that the BEM can inherit the exponential mean-square stability with a
simple proof. At last, two numerical experiments are implemented to illustrate
the reliability of the theories.
