Comparison of two numerical methods for the integration of the Takagi-Taupin equations

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), A24, 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.