Modified stochastic theta methods by ODEs solvers for stochastic differential equations

In this paper, we present a family of stochastic theta methods modified by ODEs solvers for stochastic differential equations. This class of methods constructed by adding error correction and exponential error correction terms to the traditional stochastic theta methods. Using the Itô-Taylor expansion, analyzed mean-square convergence under the Lipschitz conditions and linear growth bounds. Also, we concern mean-square stability analysis of our proposed methods. Numerical examples are presented to demonstrate the efficiency of these methods for the pathwise approximation solution of some stochastic differential equations.