Numerical Study of a One-Dimensional Poisson-Nernst–Planck Ion Channel Model By Finite Element Backward and Forward Euler Methods

Abstract

This thesis presents a numerical study of a one-dimensional Poisson-Nernst-Planck (PNP) ion channel model,which describes the transport of charged species in an electrolyte under the influence of an electric field. We develop a new numerical scheme for solving the PNP model by combining the method of lines with the finite element and Euler's forward and backward methods. We then implement the scheme based on the finite element library from the FEniCS project. To validate the accuracy of our numerical scheme, we construct an analytical solution of the PNP model with source terms. We find in numerical tests that the backward Euler method is more accurate and stable than the forward Euler method, especially for larger time steps. Furthermore, we use our numerical scheme to investigate the properties of the PNP model for an electrolyte with two ionic species. Our numerical results show that our numerical scheme can accurately capture the solution behavior of the PNP model.