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

✍ Scribed by A. Ihsan Hascelik

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 506 KB
• Volume: 223
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.01.018

✦ Synopsis

With existing numerical integration methods and algorithms it is difficult in general to obtain accurate approximations to integrals of the form

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 = ω = 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.