Premium
Comparison of two numerical methods for the integration of the Takagi–Taupin equations
Author(s) -
Nourtier C.,
Taupin D.
Publication year - 1981
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/s0021889881009709
Subject(s) - numerical integration , extension (predicate logic) , runge–kutta methods , resolution (logic) , mathematics , numerical analysis , computer science , algorithm , calculus (dental) , mathematical analysis , medicine , dentistry , artificial intelligence , programming language
Two methods for the numerical resolution of the Takagi‐Taupin equations are compared. It is shown that for a small integration step Taupin's [ Acta Cryst. (1967), 23 , 25–35] extension to two dimensions of the one‐dimensional Runge–Kutta third‐order method is more accurate than the algorithm of Authier, Malgrange & Tournarie [ Acta Cryst. (1968), A 24 , 126–136] but, for a given precision, Authier, Malgrange & Tournarie's method is faster than Taupin's so the former will usually be preferred for numerical calculation.