Robust solutions of the Yvon-Born-Green equation at very high densities

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Abstract
The Yvon-Born-Green equation under the Kirkwood superposition closure is solved for a system of hard spheres at very high densities, using a robust (second-order) convergence routine. As witnessed in earlier studies, a transition from damped oscillatory g (2)(x) functions to undamped periodic g (2)(x) functions is observed at a given value of the density parameter. However, the nature and the multiplicity of the high density solutions using the robust technique and presented herein are significantly different than before, presumably due to inadequate convergence of the earlier high density solutions.