Simulations demonstrate an accurate numerical scheme for solving charge distribution in one dimension, indicating effective predictive capabilities.
We consider a PDE which describes the evolution of an electric charge distri-bution in one spatial dimension. Due to the (singular) electrostatic interaction, the PDE is nonlocal. Moreover, the PDE describes the neutralization of charge at points where the charge distribution changes sign. Despite these complex features of the PDE, we develop a simple scheme to solve the PDE numerically. We demonstrate by means of simulations that the scheme is accurate and that it preserves the (expected) properties of the exact solution.
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Lalita et al. (2023) studied this question.
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