A simple and stable numerical solution for the population density equation.

M de Kamps

doi:10.1162/089976603322297322

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A simple and stable numerical solution for the population density equation.

M de Kamps

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Abstract

A population density description of large populations of neurons has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation (PDE). Most of the algorithms proposed to solve this PDE have used finite difference schemes. Here, I use the method of characteristics to reduce the PDE to a set of ordinary differential equations, which are easy to solve. The method is applied to leaky-integrate-and-fire neurons and produces an algorithm that is efficient and yields a stable and manifestly nonnegative density. Contrary to algorithms based directly on finite difference schemes, this algorithm is insensitive to large density gradients, which may occur during evolution of the density.

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M de Kamps. 2003. A simple and stable numerical solution for the population density equation.. https://doi.org/10.1162/089976603322297322

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