数学
偏微分方程
简单(哲学)
常微分方程
应用数学
人口
集合(抽象数据类型)
有限差分
有限差分法
微分方程
算法
数学优化
数学分析
计算机科学
认识论
哲学
社会学
人口学
程序设计语言
标识
DOI:10.1162/089976603322297322
摘要
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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