Numerical analysis of three θ methods for neutral stochastic delay differential equations

Abstract

This article focus on the numerical analysis of stochastic θ-method, split-step θ method and one-leg θ method for neutral stochastic differential equations with time lag. When some stability conditions are met, the three θ methods turned out to be mean-square stable asymptomatically. From the numerical analysis, we can see that the asymptomatically mean-square stability for both linear and nonlinear stochastic differential equations depends on the step size h and parameter θ, which numerical analysis are based on stochastic θ-method, split-step θ method and one-leg θ method.