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This paper investigates projected Euler-Maruyama method for stochastic delaydifferential equations under a global monotonicity condition. This conditionadmits some equations with highly nonlinear drift and diffusion coefficients.We appropriately generalized the idea of C-stability and B-consistency given byBeyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay.Moreover, the method is proved to be convergent with order $\frac{1}{2}$ in asuccinct way. Finally, some numerical examples are included to illustrate theobtained theoretical results.

Projected Euler method for stochastic delay differential equation under a global monotonicity condition