Educación

 

Numerical evaluation of Bessel function integrals for functions with exponential dependence

 

J. L. Luna^a, H. H. Corzo^a,b, and R. P. Sagar^a

 

^a Departamento de Química, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco No.186, Col. Vicentina, Iztapalapa 09340 México D.F., México.

^b Department of Chemistry and Biochemistry, Auburn University, Auburn, AL 36849-5312, USA.

 

Received 22 April 2013
Accepted 6 August 2013

 

Abstract

A numerical method for the calculation of Bessel function integrals is proposed for trial functions with exponential type behavior and evaluated for functions with and without explicit exponential dependence. This method utilizes the integral representation of the Bessel function to recast the problem as a double integral; one of which is calculated with Gauss-Chebyshev quadrature while the other uses a parameter-dependent Gauss-Laguerre quadrature in the complex plane. Accurate results can be obtained with relatively small orders of quadratures for the studied classes of functions.

Keywords: Bessel function integrals; Gaussian quadrature; Hankel transform; Gauss-Laguerre; Gauss-Chebyshev.

PACS: 02.30.Uu; 02.60.Jh

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

1. P. Linz, Math. Comput. 26 (1972) 509.         [ Links ]

2. J.D. Talman, J. Comput. Phys. 29 (1978) 35.         [ Links ]

3. S.M. Candel, Comput. Phys. Commun. 23 (1981) 343.         [ Links ]

4. A.V. Oppenheim, G.V. Frisk, and D.R. Martinez, J. Acoust. Soc. Am. 68 (1980) 523.         [ Links ]

5. R. Piessens, Comput. Phys. Commun. 25 (1982) 289.         [ Links ]

6. R. Piessens and M. Branders, J. Comput. Appl. Math. 11 (1984) 119.         [ Links ]

7. M. Puoskari, J. Comput. Phys. 75 (1988) 334.         [ Links ]

8. J.D. Secada, Comput. Phys. Commun. 116 (1999) 278.         [ Links ]

9. R. Piessens, The Transforms and Applications Handbook, 2nd ed. Ed. A.D. Poularikis, (CRC Press LLC, Boca Raton, 2000) Ch. 9.         [ Links ]

10. L. Knockaert, IEEE Trans. SignalProc. 48 (2000) 1695.         [ Links ]

11. M. Guizar-Sicairos, J.C. Gutierrez-Vega, J. Opt. Soc. Am. A 21 (2004) 53.         [ Links ]

12. V.K. Singh, O.P. Singh, and R.K. Pandey, Comput. Phys. Commun. 179 (2008) 424.         [ Links ]

13. V.K. Singh, O.P. Singh, and R.K. Pandey, Comput. Phys. Commun. 179 (2008) 812.         [ Links ]

14. R.P. Sagar, H. Schmider, and V.H. Smith Jr., J. Phys. A: Math. Gen. 25 (1992) 189.         [ Links ]

15. Wolfram Research, Inc., Mathematica, Version 8.0.4.0, (Champaign, IL, USA, 2011).         [ Links ]