Numerical Solutions to Neutral Stochastic Delay Differential Equations with Poisson Jumps under Local Lipschitz Condition

Abstract

Recently, Liu et al. (2011) studied the stability of a class of neutral stochastic delay differential equations with Poisson jumps (NSDDEwPJs) by fixed points theory. To the best of our knowledge to date, there are not any numerical methods that have been established for NSDDEwPJs yet. In this paper, we will develop the Euler-Maruyama method for NSDDEwPJs, and the main aim is to prove the convergence of the numerical method. It is proved that the proposed method is convergent with strong order 1/2 under the local Lipschitz condition. Finally, some numerical examples are simulated to verify the results obtained from theory.