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 Neuroscijournal_title
Journal of computational neuroscienceauthors
Stewart RD,Bair Wdoi
10.1007/s10827-008-0131-5subject
Has Abstractpub_date
2009-08-01 00:00:00pages
115-33issue
1eissn
0929-5313issn
1573-6873journal_volume
27pub_type
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