Abstract
In this paper, we consider the Poisson‐Boltzmann theory to model the electrostatic potential of a bulk electrolyte containing a single planar charged surface. In the case of a constant surface charge density, we address the problem as a ODE system by using the stability theory for autonomous dynamical systems. By stating that the surface charge density and the surface potential are non‐linearly related through the Grahame equation, we give a description of the stable manifold of the system. To solve the Grahame equation and obtain an approximation for the stable manifold, we propose a smoothing collocation method based on cubic splines, including implementation details and numerical results.
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