Application of the Cauchy integral approach to singular and highly oscillatory integrals
Makaleler > Tam Makale · 2021
Yazarlar: Idrissa Kayijuka, Suliman Alfaqeih, Turgut Öziş
International Journal of Computer Mathematics, Uluslararası, Wos, 2021, cilt 98, ss 2097-2114
DOI: 10.1080/00207160.2021.1876228
Özet
This paper presents a method that is based on the sum of line integrals for fast computation of singular and highly oscillatory integrals ∫cdG(x)eiμ(x−c)kdx,−∞>c>d>∞, and ∫−11f(x)Hl(x)eiμxdx,l=1,2,3. Where G and f are non-oscillatory sufficiently smooth functions on the interval of integration. Hl is a product of singular factors and μ≫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,∞); 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.