학술논문
Evaluation of Fresnel integrals based on the continued fractions method
Document Type
Report
Author
Source
Applied Mathematics Letters. Jan, 2005, Vol. 18 Issue 1, p23, 6 p.
Subject
Language
English
ISSN
0893-9659
Abstract
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.aml.2003.12.009 Byline: J.L. Bastardo (a), S. Abraham Ibrahim (b), P. Fernandez de Cordoba (b), J.F. Urchueguia Scholzel (c), Yu.L. Ratis (d) Abstract: We present a simple algorithm for evaluating Fresnel integrals based on the continued fractions method: we use the relation between these integrals and first-kind Bessel functions of fractional order, and we apply a fast code to calculate them based on the continued fractions method. This latter code is especially useful for evaluating high order Bessel functions because it does not require recalculations using normalization relations. Comments on the same procedure but using Miller's algorithm to evaluate the required Bessel functions are presented and a comparison with a standard code for evaluating Fresnel integrals (Numerical Recipes program FRENEL) is provided. Author Affiliation: (a) Departamento de Computacion y Sistemas, Escuela de Ingenieria y Ciencias Aplicadas, Nucleo de Anzoategui - Universidad de Oriente, Puerto La Cruz, Venezuela (b) Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia, Spain (c) Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, Valencia, Spain (d) Samara State Aerospace University, Moskovskoye Shosse 34, 443086-Samara, Russia Article History: Received 1 December 2002; Accepted 1 December 2003