Studying mean-square stability of numerical method applied for solving models of stochastic differential equations

Abstract

In this paper, Herimte approximations with two collocation points are used for the numerical simulation of stochastic of differential equations (SDE), and continuous wiener processes are computed by computer discrete simulations. The mean-square stability was studied by applying the proposed technique with the Wiener process on a test stochastic differential equation. The study shows that the proposed method is mean-square stability, strongly convergent from order third and locates large stability regions of method at the real plane. Moreover, the scheme is tested on three problems to illustrate the applicability and efficiency of the purposed technique. Comparisons of our results with others methods, it reveals that our method is better than others.