A new method of solving the liquid structure integral equations

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Abstract
We present a new method of obtaining numerical solutions to the Percus-Yevick and hypernetted chain equations for liquid structure. The method, which is rapidly convergent and very stable, is a hybrid of the traditional iterative scheme and the Newton-Raphson technique. We show by numerical tests for typical potentials that the method gives well-converged solutions in 20 or 30 iterations even for very high densities. The number of iterations needed is insensitive to the choice of initial estimate, even if this is extremely inaccurate.