The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays

The main aim of this paper is to investigate the strong convergence order for the truncated Euler-Maruyama (TEM) method to solve stochastic differential delay equations (SDDEs) with multiple time delays and super-linearly growing coefficients. The strong L^p (1 ≤ p < 2) convergence rate of the TEM method under the one-sided polynomial growth condition is first established. Imposing additional conditions on the diffusion coefficient, the p-th moment uniform boundedness of both the exact and approximate solutions is then proved. Next, we show that the strong order of L^q-convergence can be arbitrarily close to 1/2 for 2 ≤ q ≤ p. Several examples and a numerical simulation are provided to illustrate the main results at the end.