Condensed Matter


The Dirichlet and the Neumann Boundary Conditions May not Produce Equivalent Solutions to the Same Electrostatic Problem

Authors: Rajib Chakraborty

Electrostatic problems are widely solved using two types of boundary conditions (BC), namely, the Dirichlet condition (DC) and Neumann condition (NC). The DC specifies values of electrostatic potential ($\psi$), while the NC specifies values of $\nabla \psi$ at the boundaries. Here we show that DC and NC may not produce equivalent solutions to a given problem; we demonstrate it with a particular problem: 1-D linearized Poisson-Boltzmann equation (PBE), which has been regularly used to find the distribution of ionic charges within electrolyte solutions. Our findings are immediately applicable to many other problems in electrostatics.

Comments: 4 Pages.

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Submission history

[v1] 2017-04-25 16:11:18
[v2] 2017-09-02 06:50:51

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