On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]

Authors:
A. Ihsan Hascelik
Affiliations:
University of Gaziantep, Department of Mathematics, Gaziantep 27310, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

With existing numerical integration methods and algorithms it is difficult in general to obtain accurate approximations to integrals of the form @!"0^1f(x)sin(@wx^r)dxor@!"0^1f(x)cos(@wx^r)dx,(r0) where f is a sufficiently smooth function on [0, 1]. Gautschi has developed software (as scripts in Matlab) for computing these integrals for the special case r=@w=1. In this paper, an algorithm (as a Mathematica program) is developed for computing these integrals to arbitrary precision for any given values of the parameters in a certain range. Numerical examples are given of testing the performance of the algorithm/program.