Approximate calculation of double integrals of highly oscillating functions of general type using the cubature formula of optimal order of accuracy on a class of differentiable functions

The problem of approximating double integrals of highly oscillating functions of general type (irregular case) is considered. A cubature formula is constructed that uses O.M. Lytvyn's information operators and piecewise linear splines as auxiliary functions. Information about the functions is provided by the corresponding values on the lines. It is proved that the proposed cubature formula is optimal in order of accuracy on the class of differentiable functions. Keywords: optimal numerical integration, highly oscillating functions of general type, O.M. Lytvyn’s information operators, cubature formula optimal in order of accuracy, differential functions of two variables.