Compensated two-step Maruyama methods for stochastic differential equations with Poisson jumps

In this article we present the compensated two-step Maruyama methods for the stochastic differential equations with Poisson jumps. Mean-square (M-S) order convergence 1/2 is established and M-S stability analysis are displayed. In particular, compensated two-step Maruyama methods of Adams type are considered, their linear M-S stability regions compared with compensated Euler- Maruyama method (EM) are plotted. Numerical results show the M-S convergence and stability are given.