ON THE APPLICATION OF QUADRATURE FORMULAS FOR CALCULATING INTEGRALS OF ARBITRARY MULTIPLICITY - S.K. Zamanova; A.D. Muradov (Academic Scientific Journal of Computer Science, 2019)
In this paper, we consider the calculation of integrals of arbitrary multiplicity by the methods of nonuniform grids, Monte Carlo and optimal coefficients. A comparative analysis of these numerical methods for integrating multiple integrals was made. It was established that the method of optimal coefficients had an advantage compared to other methods. It is shown that the use of uneven and parallelepipedal grids is the basis of almost all results obtained in the field of application of theoretic – numerical methods to the problems of approximate analysis. It is established that interpolation of functions of several variables by theoretic-numerical grids allows to receive interpolation formulas, accuracy of which rises with increase of smoothness of functions. The number of variables in this case has no significant effect on the order of the residual member.