Calculation of the multidimensional cubatures in unit hypercube is a complex problem of numerical methods, and its application value is great. This paper compares various calculation methods: product of regular one-dimensional grid formulae, classical Monte Carlo method using pseudorandom points and the Sobol sequences. It is suggested to use not any Sobol sequences, but only the ones with magic numbers N equal to powers of 2. In addition, the shifted Sobol points are proposed: all coordinates of the magic Sobol points are simultaneously increased by 1/(2N). Comparisons on the test showed that the latter method is significantly more accurate than all the others.

multidimensional cubatures, Monte Carlo method, Sobol sequences, magic numbers, shifted Sobol points

Mathematical modelling in actual problems of science and technics

Belov Alexander Alexandrovich,  ,  orcid.org/0000-0002-0918-9263,  M.V. Lomonosov MSU, Faculty of Physics; PFUR

Kalitkin Nikolaj Nikolaevich,  ,  orcid.org/0000-0002-0861-1792,  KIAM RAS

Tintul Maksim Alexandrovich,  ,  orcid.org/0000-0002-5466-1221,  M.V. Lomonosov MSU, Faculty of Physics