DQAINF swMATH ID: 2646 Software Authors: Espelid, T.O.; Overholt, K.J. Description: DQAINF: An algorithm for automatic integration of infinite oscillating tails. The paper describes a quadrature routine designed to integrate a (scalar or vector) function with a certain type of infinite oscillating, decaying tails over an infinite interval. The algorithm is based on the assumption that the oscillating behavior is due to the superposition of periodic functions which change sign when evaluated at points of distance half a period. Hence, following the basic ideas of J. N. Lyness [J. Comp. Appl. Math. 12/13, 109-117 (1985; Zbl 0574.65013)], partitioning the original integral into an infinite series of integrals all of same interval length yields close relations to alternating series, and the Euler transformation (together with some modifications) implies very stable schemes for accelerated approximations. A FORTRAN subroutine for the algorithm is described in detail. Six examples show the efficiency of the method. Homepage: http://www.springerlink.com/content/f62411786x607624/fulltext.pdf Programming Languages: FORTRAN Keywords: quadrature formulas; Riemann zeta function; infinite oscillating; decaying tails; infinite interval; algorithm; superposition of periodic functions; Euler transformation; FORTRAN subroutine; Fresnel integrals Related Software: DQAINT; QUADPACK; Algorithm 639; HURRY; Mathematica; pchip; Clenshaw-Curtis; UNCMND Cited in: 8 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year DQAINF: An algorithm for automatic integration of infinite oscillating tails. Zbl 0811.65017Espelid, T. O.; Overholt, K. J. 1994 all top 5 Cited by 11 Authors 2 Espelid, Terje O. 2 Sauter, Thilo 1 Hasegawa, Takemitsu 1 Luo, Xiaolin 1 Michalski, Krzysztof A. 1 Overholt, K. J. 1 Shevchenko, Pavel V. 1 Sidi, Avram 1 Xu, Jianxin 1 Yan, Rui 1 Zhang, Weinian Cited in 5 Serials 4 Numerical Algorithms 1 Applied Numerical Mathematics 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Scientific Computing 1 IEEE Transactions on Antennas and Propagation all top 5 Cited in 6 Fields 6 Numerical analysis (65-XX) 3 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) Citations by Year