Spiking neural network simulation: numerical integration with the Parker-Sochacki method.

Abstract:

:Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. The method has been limited to polynomial equations, but we present division and power operations that expand its scope. We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.

journal_name

J Comput Neurosci

authors

Stewart RD,Bair W

doi

10.1007/s10827-008-0131-5

subject

Has Abstract

pub_date

2009-08-01 00:00:00

pages

115-33

issue

1

eissn

0929-5313

issn

1573-6873

journal_volume

27

pub_type

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