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.
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References in zbMATH (referenced in 11 articles , 1 standard article )
Showing results 1 to 11 of 11.
- Luo, Xiaolin; Shevchenko, Pavel V.: A short tale of long tail integration (2011)
- Espelid, Terje O.: Algorithm 868: Globally doubly adaptive quadrature -- reliable Matlab codes. (2007)
- Espelid, T.O.: Computation of an infinite integral using series acceleration (2005)
- Xu, Jian-Xin; Yan, Rui; Zhang, Weinian: An algorithm for Melnikov functions and application to a chaotic rotor (2005)
- Espelid, Terje O.: Doubly adaptive quadrature routines based on Newton-Cotes rules (2003)
- Sauter, Thilo: Computation of irregularly oscillating integrals (2000)
- Sauter, Thilo: Fourier transforms of slowly converging functions exemplified by electromagnetic wave propagation in evanescent structures (1999)
- Michalski, Krzysztof A.: Extrapolation methods for Sommerfeld integral tails (1998)
- Hasegawa, Takemitsu; Sidi, Avram: An automatic integration procedure for infinite range integrals involving oscillatory kernels (1996)
- Espelid, T.O.; Overholt, K.J.: DQAINF: An algorithm for automatic integration of infinite oscillating tails (1994)
- Espelid, Terje O.: DQAINT: An algorithm for adaptive quadrature over a collection of finite intervals (1992)