Convergence and stability of balanced methods for stochastic delay integro-differential equations

This paper deals with a family of balanced implicit methods for the stochastic delay integro-differential equations. It is shown that the balanced methods, which own the implicit iterative scheme in the diffusion term, give strong convergence rate of at least 1/2. It proves that the mean-square stability for the stochastic delay integro-differential equations is inherited by the strong balanced methods and the weak balanced methods with sufficiently small stepsizes. Several numerical experiments are given for illustration and show that the fully implicit methods are superior to those of the explicit methods in terms of mean-square stabilities.