CONVERGENCE AND STABILITY OF IMPROVED EULER-MARUYAMA APPROXIMATION METHOD FOR STIFF STOCHASTIC DIFFERENTIAL EQUATIONS

Stiff stochastic differential equations are usually solved numerically by (semi- )implicit methods, and many numerical methods for solving of these case of stochastic differential equations have been designed. This paper presents a family of explicit im proved Euler-Maruyama approximation method for solution of the stiff stochastic differ ential equations. We apply the linear growth bounds and Lipschitz conditions on the drift and diffusion coefficients for analytical study of the stochastic differential equation. One of the important points in the study of stochastic differential equations is the inves tigation of numerical solution behavior from the point of view of convergence. The strong mean-square convergence of our new method is analyzed. Another important issue for stiff stochastic differential equations is to check the stability of a numerical method. To study the mean-square stability property of our method, we consider a one-dimensional linear Itô test stochastic differential equation with a single noise term. A numerical ex ample is given to illustrate the accuracy and efficiency of the proposed method