Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

Abstract

An efficient recursive procedure to solve the density profile equation in the classical density functional theory (DFT) using an inverse Broyden method is described. The present iterative procedure is free of calculation of the Jacobian matrix, and its inversion unavoidable for the well-known Newton-Raphson (NR) method and its variants. Numerical calculation indicates that only the approximate solution and iterative matrix of the lower bulk density case are employed as the corresponding initial guesses of the higher bulk density case, the present recursive procedure can converge quickly to the physical solution with an accuracy of epsilon = 10(-14); therefore, the procedure provides an efficient numerical algorithm for the theory in which acquirement of a density profile of high accuracy is a key step. Extensive numerical calculation shows the advantage of the present inverse Broyden method over Broyles' mixing procedure and a modified Powell hybrid algorithm (a variation of the NR method).