The Three-Step Strong Numerical Methods of the Orders of Accuracy 1.0 and 1.5 for Ito Stochastic Differential Equations

摘要

This work deals with the three-step strong numerical methods of the orders of accuracy 1.0 and 1.5 for Ito stochastic differential equations. We propose the explicit and implicit three-step numerical schemes, as well as the three-step numerical schemes of a Runge―Kutta type. The convergence of the considered numerical methods is proved theoretically and illustrated by numerical experiments.