  The article is devoted to comparative analysis of the efficiency of
application of Legendre polynomials and trigonometric functions to the
numerical integration of Ito stochastic differential equations in the framework
of the method of approximation of iterated Ito and Stratonovich stochastic
integrals based on generalized multiple Fourier series. On the example of
iterated Ito stochastic integrals of multiplicities 1 to 3, included in the
Taylor-Ito expansion, it is shown that expansions of stochastic integrals based
on Legendre polynomials are much easier and require significantly less
computational costs compared to their analogues obtained using the
trigonometric system of functions. The results of the article can be useful for
construction of high-order strong numerical methods for Ito stochastic
differential equations.
