DQAINF: An algorithm for automatic integration of infinite oscillating tails

DOI10.1007/BF02145697zbMath0811.65017MaRDI QIDQ1339045

K. J. Overholt, Terje O. Espelid

Publication date: 2 May 1995

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

algorithmRiemann zeta functionquadrature formulasinfinite intervalFORTRAN subroutineFresnel integralsEuler transformationinfinite oscillating, decaying tailssuperposition of periodic functions

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (5)

A short tale of long tail integration ⋮ DQAINF ⋮ An automatic integration procedure for infinite range integrals involving oscillatory kernels ⋮ Computation of an infinite integral using series acceleration ⋮ Computation of irregularly oscillating integrals

Uses Software

• HURRY
• QUADPACK
• DQAINT
• Algorithm 639

Cites Work

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• Practical error estimation in adaptive multidimensional quadrature routines
• Integrating some infinite oscillating tails
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Extrapolation methods theory and practice
• Indefinite integration of oscillatory functions by the Chebyshev series expansion
• Tables for the Rapid and Accurate Numerical Evaluation of Certain Infinite Integrals Involving Bessel Functions
• A Method for the Numerical Evaluation of Finite Integrals of Oscillatory Functions
• HURRY: An Acceleration Algorithm for Scalar Sequences and Series
• Algorithm 639
• On the Construction of Higher Degree Three-Dimensional Embedded Integration Rules
• Extrapolation Methods for Oscillatory Infinite Integrals
• Error estimation in automatic quadrature routines
• The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
• Development of non-linear transformations for improving convergence of sequences

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