Leila Torkzadeh - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran
Hassan Ranjbar - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran

In this paper, we improved the split step vartheta method to solve the stochastic differential equations. The strong convergence of this approximation for stochastic differential equations, whose drift and diffusion coefficients are globally Lipschitz continuous, are investigated. Furthermore, we analyze the stability in the mean square sense of our scheme by scalar stochastic differential equation with multi dimensional Wiener processes. The study of stability shows the mean square stability of the method for vartheta in [۱/۲, ۱] . Finally, we present some numerical examples to describe the methodology and implementation of the split step vartheta method to solve linear and nonlinear one dimensional stochastic differential equations and the Lotka-Volterra stochastic system.

Stochastic differential equations, Split step vartheta method, Strong convergence, Mean square stability