Reliable operations on oscillatory functions

Approximate p-point Leibniz derivation formulae as well as interpolatory Si mpson quadrature sums adapted to oscillatory functions of constant frequenc y parameter are discussed. Both theoretical considerations and numerical ev idence concerning the dependence of the discretization errors on the freque ncy parameter of the oscillatory functions show that the accuracy gain of t he present formulae over those based on the exponential fitting approach [L . Ixaru, Computer Physics Communications 105 (1997) 1-19] is overwhelming. (C) 2000 Elsevier Science B.V. All rights reserved.