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The article is devoted to the construction of explicit one-step strongnumerical methods with the orders 2.0 and 2.5 of convergence for Ito stochasticdifferential equations with multidimensional non-commutative noise. We considerthe numerical methods based on the unified Taylor-Ito and Taylor-Stratonovichexpansions. For the numerical modeling of iterated Ito and Stratonovichstochastic integrals of multiplicities 1 to 5 we apply the method of multipleFourier-Legendre series converging in the sense of norm in Hilbert space$L_2([t, T]^k),$ $k=1,\ldots,5$. The article is addressed to engineers who usenumerical modeling in stochastic control and for solving the non-linearfiltering problem. The article will be interesting to scientists who working inthe field of numerical integration of stochastic differential equations.

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Explicit One-Step Strong Numerical Methods of Orders 2.0 and 2.5 for Ito  Stochastic Differential Equations Based on the Unified Taylor-Ito and  Taylor-Stratonovich Expansions