Optimal-By-Order Quadrature Formulae for Fast Oscillatory Functions with Inaccurately Given A Priori Information

Melnik, K.N. and Melnik, R.V.N.

Journal of Computational and Applied Mathematics,  110, 45--72, 1999

Abstract:

In this article, the authors construct optimal-by-order quadrature formulae for integration of fast oscillatory functions in interpolational classes $C_{l,L,N}^l$ and $C_{l, L, N, epsilon}^l$. 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.