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DINAME2019
DINAME2019
An FFT-based Generalization of the ε-algorithm for the Integration of Oscillatory-Decaying Functions with Multiple Frequencies
Submission Author:
Iago Cavalcante , SP
Co-Authors:
Iago Cavalcante, Josue Labaki
Presenter: Iago Cavalcante
doi://10.26678/ABCM.DINAME2019.DIN2019-0005
Abstract
This paper presents a method for numerical integration of improper integrals with oscillatory-decaying functions containing one or more than one frequency of oscillation. These integrals occur in the solution of a wide variety of dynamic problems; especially those in which some space transform is involved in the solution of the equations of motion. A classical integration method for the case of an integrand with a single oscillatory frequency is to extrapolate the integral from a sequence of partial sums over finite subintervals, in the framework of Euler’s convergent series. This integration scheme, however, is unable to deal with the case in which the integrand has more than one oscillatory frequency. The integration scheme presented in this paper consists in using a fast Fourier transform to select appropriate endpoints to divide integrands with multiple oscillatory frequencies, together with a robust series extrapolation through the ε-algorithm. The method is used to integrate transcendental functions of multiple oscillatory frequencies, including a case in which a closed-form expression for the integrand is not known. The results are compared with classical adaptive quadrature implementations.
Keywords
Numerical Integration, fast Fourier transform, ε-algorithm, multiple oscillatory frequencies
