A User-Friendly Extrapolation Method for Oscillatory Infinite Integrals

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 ...

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...

Extrapolation Methods for Oscillatory Infinite Integrals

The non-linear transformations for accelerating the convergence of slowly convergent infinite integrals due to Levin & Sidi (1975) are modified in two ways. These modifications enable one to eval uate accurately some oscillatory infinite integrals with less work. Special emphasis is placed on the evaluation of Fourier and Hankel transforms and some simple algorithms for them are given. Converge...

A User - Friendly Extrapolation Method for Oscillat

The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation

Recently the author has given two modifications of a nonlinear extrapolation method due to Levin and Sidi, which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity. In this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and...