2023/04/10 by Chao, Zhen, Geng, Weihua, Krasny, Robert · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2304.04371
An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green's 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method's 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K+ ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.