A New Method for the Numerical Solution of Integral Equation Approximations 1

A new numerical technique for solving the Ornstein-Zernike equation is described. It is particularly useful in solving the Ornstein Zernike equation for approximations and pair potentials (such as the Percus-Yevick and mean spherical approximations for finite ranged potentials) which imply a finiteranged direct correlation function since for such approximations the numerical technique is essentially exact. The only approximation involved in such cases is the discretization of direct and total correlation functions over the finite range on which the direct correlation function is nonzero. Thus, the new method avoids truncation of the total correlation function and should permit the critical point and spinodal curve to be mapped out with greater accuracy than is permitted by existing methods. Preliminary explorations on the stability and accuracy of the method are described.