A user-friendly method for computing indefinite integrals of oscillatory functions

A user-friendly extrapolation method for computing infinite range integrals of products of oscillatory functions

where s is an arbitrary integer, φ̂(x) and θ̂ (x) are real polynomials in x , φ̂(x) ≡ 0 being possible, exp[φ̂(x)] is bounded at infinity and R(x) and gj (x) are smooth functions that have asymptotic expansions of the forms R(x) ∼ ∑∞ i=0 bi x −i and gj (x) ∼ ∑∞ i=0 c ± j i x δ j−i as x → ∞, with arbitrary and δ j . We denote the class of such functions by B̃(s). These integrals may converge or diver...

A User-Friendly Extrapolation Method for Oscillatory Infinite Integrals

In a recent publication [4] the author developed an extrapolation method, the ^-transformation, for the accurate computation of convergent oscillatory infinite integrals. In yet another publication [6] this method was shown to be applicable to divergent oscillatory infinite integrals that are defined in the sense of summability. The application of the VK-transformation involves some asymptotic ...

On High Precision Methods for Computing Integrals of Oscillatory Functions*

A short account of the most important methods for the evaluation of integrals of oscillatory functions and an unified approach for such a purpose are given.

On the convergence of the method for indefinite integration of oscillatory and singular functions

We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in [P. Keller, A method for indefinite integration of oscillatory and singular functions, Numerical Algorithms 46(3) (2007), 219–251]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a f...

A User - Friendly Extrapolation Method for Oscillat