Efficient solution of liquid state integral equations using the Newton-GMRES algorithm Original Research Article

We present examples of the accurate, robust and efficient solution of Ornstein-Zernike type integral equations which describe the structure of both homogeneous and inhomogeneous fluids. In this work we use the Newton-GMRES algorithm as implemented in the public-domain nonlinear Krylov solvers NKSOL [] and NITSOL []. We compare and contrast this method with more traditional approaches in the literature, using Picard iteration (successive-substitution) and hybrid Newton-Raphson and Picard methods, and a recent vector extrapolation method []. We find that both the performance and ease of implementation of these nonlinear solvers recommend them for the solution of this class of problem.