Application of the Cauchy integral approach to singular and highly oscillatory integrals
Küçük Resim Yok
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This paper presents a method that is based on the sum of line integrals for fast computation of singular and highly oscillatory integrals integral(c) (d) G(x) e(i mu(x-c)k) dx, -infinity > c > d > infinity, and integral(1)(-1) f (x)H-l(x) e(i mu x) dx, l = 1, 2, 3. Where G and f are non-oscillatory sufficiently smooth functions on the interval of integration. H-l is a product of singular factors and mu >> 1 is an oscillatory parameter. The computation of these integrals requires f and G to be analytic in a large complex region C accommodating the interval of integration. The integrals are changed into a problem of integrals on [0, infinity); which are later computed using the generalized Gauss-Laguerre rule or by the construction of Gauss rules relative to a Freud weights function e-xk with k positive. MATHEMATICA programming code, algorithms and illustrative numerical examples are provided to test the efficiency of the presented experiments.
Açıklama
Anahtar Kelimeler
Highly oscillatory integrals, Gauss quadrature rules, Numerical steepest descent method, Gauss-Laguerre quadrature rule, Chebyshev algorithm
Kaynak
International Journal of Computer Mathematics
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
