Solution of the Poisson-Boltzmann equation through the use of pseudo-dynamic simulation method

An approach to solve numerically the nonlinear Poisson-Boltzmann equation (PBE) is proposed. Departing from the fact that the PBE can be seen as a reaction-diffusion equation, the numerical method consists in a discretization of the domain by means of cells in which advection and reaction are balanced in such a way that the procedure resembles the PBE. In an homogeneous domain, the numerical procedure reduces to a pseudo-dynamic finite-differences method. In order to show the effectiveness of the numerical procedure, we illustrate its application with two examples: (a) an infinite plate and (b) two interacting cylinders immersed in an electrolyte solution.