Optimal-by-order quadrature formulae for fast oscillatory functions with inaccurately given a priori information

In this article, the authors construct optimal-by-order quadrature formulae for integration of fast oscillatory functions in interpolational classes C1, L, N1 and C1, L, N, ε1. The construction of efficient formulae for numerical integration of fast oscillatory functions is based on the application of the residual method and the method of quasi-solutions. Both cases, weak and strong oscillations, are considered. Results of numerical examples are presented.