Balanced implicit methods with strong order 1.5 for solving stochastic differential equations

The aim of this article is to propose a family of balanced implicit methods and split-step balanced implicit methods for solving Itô stochastic differential equations. These numerical methods represent a class of highly efficient linear-implicit schemes which covered the implicitness in the stochastic terms. The convergence in mean-square with strong order 1.5 and the asymptotic mean-square stability properties of these methods are analysed. What is more, the linear mean-square stability regions of some proposed methods are given. Several numerical examples are carried out to illustrate the theoretic findings.