title: Physical approach to analytic simulation of Fresnel integrals.
abstract: Fresnel integrals continue to find new applications in various areas of human activity, including technology and music. However, performing calculations with them is often hindered by a mathematical peculiarity of these integrals, which is the rapidly oscillating functions of the basic variable. This circumstance complicates the numerical calculations when these integrals need additional integral transformation: convolution, Fourier transform, etc. The suggested solution of the problem consists of replacement of the complex Fresnel integral by a single rational function that simulates this integral in the entire area of its existence with an accuracy up to 10(-6). The advantages of the suggested approach are confirmed by the concrete example.
authors.affiliation: International Center "Institute of Applied Physics", National Academy of Sciences Ukraine, Kiev, Ukraine. anokhov@i.kiev.ua
authors.forename: Sergey
authors.initials: S
authors.lastname: Anokhov