  The article is devoted to explicit one-step numerical methods with strong
orders 1.0, 1.5, and 2.0 of convergence for Ito stochastic differential
equations with multidimensional and non-commutative noise. For numerical
modeling of iterated Ito stochastic integrals with multiplicities 1 to 4 we use
the method of multiple Fourier-Legendre series converging in the sense of norm
in Hilbert space $L_2([t, T]^k),$ $k=1,2,3,4.$ The article is addressed to
engineers who use numerical modeling in stochastic control and for solving the
nonlinear filtering problem.
