Optimal-by-order quadrature formulae for fast oscillatory functions with inaccurately given a priori information (Q1807765)

In this very interesting and well-written paper, the authors construct optimal-by-order quadrature formulae for integration of fast oscillatory functions in the interpolational classes \(C^1_{1,L,N}\) and \(C^1_{1,L,N,\varepsilon}\). The construction is based on the application of the residual method and the method fo quasi-solutions. Numerical examples are considered.