One of the key tasks in modern applied mathematics, without which modeling and analysis of complex processes is impossible, in particular in mathematicalphysics and digital image processing, is the numerical integration of functions of many variables. Often, the analytical calculation of multivariableintegrals is impossible due to the complexity of the functions themselves or the integration domain, which necessitates the use of effective numerical methods. The main problem of numerical integration of functions of many variables is the growth of computational costs with increasing dimension of the integration domain - the so-called “curse of dimension”. This leads to the search for efficient methods that allow to maintain a balance between computational complexity and accuracy of results. Of particular interest are numerical integration methods developed using information operators that restore intermediate values of quantities based on a given set of known values of a function of many variables at points, on lines, planes, etc. On the basis of such operators, economical schemes for interpolating functions of two and three variables are built. The use of economical schemes in the numerical integration of functions of several variables allows to calculate multidimensional integrals with a predetermined accuracy with less data compared to classical methods. The purpose of this article is to demonstrate the use of economical interpolation schemes for the approximate calculation of double integrals, as well as two-dimensional integrals of highly oscillating functions of general type.
Nechuiviter et al. (Mon,) studied this question.