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Journal of Computational Neuroscience

, Volume 26, Issue 3, pp 445–457 | Cite as

A finite volume method for stochastic integrate-and-fire models

  • Fabien MarpeauEmail author
  • Aditya Barua
  • Krešimir Josić
Article

Abstract

The stochastic integrate and fire neuron is one of the most commonly used stochastic models in neuroscience. Although some cases are analytically tractable, a full analysis typically calls for numerical simulations. We present a fast and accurate finite volume method to approximate the solution of the associated Fokker-Planck equation. The discretization of the boundary conditions offers a particular challenge, as standard operator splitting approaches cannot be applied without modification. We demonstrate the method using stationary and time dependent inputs, and compare them with Monte Carlo simulations. Such simulations are relatively easy to implement, but can suffer from convergence difficulties and long run times. In comparison, our method offers improved accuracy, and decreases computation times by several orders of magnitude. The method can easily be extended to two and three dimensional Fokker-Planck equations.

Keywords

Stochastic integrate and fire model Numerical methods 

Notes

Acknowledgements

We thank Cheng Ly, Roberto Fernández Galán and Brent Doiron for helpful discussions. This research was supported by NSF grants DMS-0604429 and DMS-0817649, and a Texas ARP/ATP award.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Fabien Marpeau
    • 1
    Email author
  • Aditya Barua
    • 1
  • Krešimir Josić
    • 1
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA

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