ON THE APPLICATION OF QUADRATURE FORMULAS FOR CALCULATING INTEGRALS OF ARBITRARY MULTIPLICITY
Ключевые слова:
theoretic-numerical method, quadrature formula, method of optimal coefficients, multiple integrals.Аннотация
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.
