Abstract
This paper presents a method that is based on the sum of line integrals for fast computation of singular and highly oscillatory integrals , and . Where G and f are non-oscillatory sufficiently smooth functions on the interval of integration. is a product of singular factors and 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 ; which are later computed using the generalized Gauss-Laguerre rule or by the construction of Gauss rules relative to a Freud weights function with k positive. MATHEMATICA programming code, algorithms and illustrative numerical examples are provided to test the efficiency of the presented experiments.
2010 Mathematics Subject Classification:
Disclosure statement
No potential conflict of interest was reported by the author(s).