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

computational mathematics and mathematical physics

Comparative Analysis of the Efficiency of Application of Legendre  Polynomials and Trigonometric Functions to the Numerical Integration of Ito  Stochastic Differential Equations