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The Poisson-Nernst-Planck (PNP) system is a widely accepted model forsimulation of ionic channels. In this paper, we design, analyze, andnumerically validate a second order unconditional positivity-preserving schemefor solving a reduced PNP system, which can well approximate the threedimensional ion channel problem. Positivity of numerical solutions is proven tohold true independent of the size of time steps and the choice of the Poissonsolver. The scheme is easy to implement without resorting to any iterationmethod. Several numerical examples further confirm the positivity-preservingproperty, and demonstrate the accuracy, efficiency, and robustness of theproposed scheme, as well as the fast approach to steady states.

Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system