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Efficiency in the calculation of absorption corrections for cylinders
Author(s) -
Ida Takashi
Publication year - 2010
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889810021199
Subject(s) - numerical integration , quadrature (astronomy) , gaussian quadrature , absorption (acoustics) , legendre polynomials , numerical analysis , physics , computational physics , mathematics , mathematical analysis , optics , integral equation , nyström method
Efficiency in the numerical calculation of absorption corrections for cylinders has been examined. Two mathematical expressions for the correction factors have been evaluated by two methods for numerical integration. It has been found that the Gauss–Legendre quadrature applied to the formula proposed by Thorkildsen & Larsen [ Acta Cryst. (1998), A 54 , 172–185] gives results with relative errors ≤10 −6 , using 12 × 12 terms in the numerical integration. The conventional approach, using Simpson's method in conjunction with the formula given by Dwiggins [ Acta Cryst. (1975), A 31 , 146–148] for the absorption correction, is far less efficient.