In this paper, we study the convergence of explicit numerical methods in strong sense for stochastic delay differential equations (SDDEs) with super-linear growth coefficients. Under non-globally Lipschitz conditions, a fundamental theorem on convergence has been constructed to elaborate the relationship of convergence rate between the local truncated error and the global error of one-step explicit methods in the sense of $p$th moments. A class of balanced Euler schemes has been presented and the boundedness of numerical solutions has been proved. By using the fundamental theorem, we prove that the balanced Euler scheme is of 0.5 order convergence in mean-square sense. Numerical examples verify the theoretical predictions.

在本文中，我们研究具有超线性增长系数的随机时滞微分方程（SDDE）的强数值显式数值方法的收敛性。在非全局Lipschitz条件下，构造了收敛的基本定理，以阐述局部截断误差与单步显式方法的全局误差之间的收敛速度之间的关系。$p$时刻。提出了一类平衡欧拉格式，并证明了数值解的有界性。通过使用基本定理，我们证明了均衡的欧拉方案在均方意义上具有0.5阶收敛性。数值例子验证了理论预测。