Numerical evaluation of integrals containing a spherical Bessel function by product integration

Journal Article · Wed Jul 01 04:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525061· OSTI ID:6186584

Lehman, D R; Parke, W C; Maximon, L C

A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented.

• Research Organization: Department of Physics, The George Washington University, Washington, D. C. 20052
• OSTI ID: 6186584
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
BESSEL FUNCTIONS
FUNCTIONS
INTEGRALS
MATHEMATICAL LOGIC
MATHEMATICS
NUMERICAL ANALYSIS
POLYNOMIALS