On Numerical Modeling of the Multidimensional Dynamic Systems under Random Perturbations with the 1.5 and 2.0 Orders of Strong Convergence

Abstract

The paper was devoted to developing numerical methods with the orders 1.5 and 2.0 of strong convergence for the multidimensional dynamic systems under random perturbations obeying stochastic differential Ito equations. Under the assumption of a special mean-square convergence criterion, attention was paid to the methods of numerical modeling of the iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 4 that are required to realize the aforementioned numerical methods.