AN EFFICIENT GAUSS-NEWTON-LIKE METHOD FOR THE NUMERICAL-SOLUTION OF THE ORNSTEIN-ZERNIKE INTEGRAL-EQUATION FOR A CLASS OF FLUID MODELS

A numerical algorithm for solving the Ornstein-Zernike (OZ) integral e quation of statistical mechanics is described for the class of fluids composed of molecules with axially symmetric interactions. Since the O Z equation is a nonlinear second-kind Fredholm equation whose key feat ure for the class of problems of interest is the highly computationall y intensive nature of the kernel, the general approach employed in thi s paper is thus potentially useful for similar problems with this char acteristic. The algorithm achieves a high degree of computational effi ciency by combining iterative linearization of the most complex portio n of the kernel with a combination of Newton-Raphson and Picard iterat ion methods for the resulting approximate equation. This approach make s the algorithm analogous to the approach of the classical Gauss-Newto n method for nonlinear regression, and we call our method the GN algor ithm. An example calculation is given illustrating the use of the algo rithm for the hard prolate ellipsoid fluid and its results are compare d directly with those of the Picard iteration method. The GN algorithm is four to ten times as fast as the Picard method, and we present evi dence that it is the most efficient general method currently available . (C) 1994 Academic Press, Inc.