Reliable operations on oscillatory functions Original Research Article

Approximate p-point Leibniz derivation formulae as well as interpolatory Simpson quadrature sums adapted to oscillatory functions of constant frequency parameter are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulae over those based on the exponential fitting approach [L. Ixaru, Computer Physics Communications 105 (1997) 1–19] is overwhelming.