Two-step strong order 1.5 schemes for stochastic differential equations

A general class of linear two-step schemes for solving stochastic differential equations is presented. Necessary and sufficient conditions on its parameters to obtain mean square order 1.5 are derived. Then the linear stability of the schemes is investigated. In particular, among others, the stability regions of generalizations of the classical two-step schemes Adams-Bashford, Adams-Moulton, and BDF are obtained.