On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems

Kahaner, David K.; Lawkins, W.F.; Thompson, Sharon

doi:10.1016/0377-0427(89)90334-8

Cited by 5 publications

(1 citation statement)

References 8 publications

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“…If the time of the threshold crossing cannot be determined analytically, the actual threshold finding algorithm causes jitter by inexact computation of the crossing. Since root finding on ODE solutions is a well understood problem (Hiebert and Shampine 1980;Thompson and Tuttle 1984;Kahaner et al 1989), there are plenty of actual solutions that offer arbitrary accuracy. Relating to Eq.…”

Section: Review Of Timing Errorsmentioning

confidence: 99%

Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks

Henker¹,

Partzsch²,

Schüffny³

2011

J Comput Neurosci

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With the various simulators for spiking neural networks developed in recent years, a variety of numerical solution methods for the underlying differential equations are available. In this article, we introduce an approach to systematically assess the accuracy of these methods. In contrast to previous investigations, our approach focuses on a completely deterministic comparison and uses an analytically solved model as a reference. This enables the identification of typical sources of numerical inaccuracies in state-of-the-art simulation methods. In particular, with our approach we can separate the error of the numerical integration from the timing error of spike detection and propagation, the latter being prominent in simulations with fixed timestep. To verify the correctness of the testing procedure, we relate the numerical deviations to theoretical predictions for the employed numerical methods. Finally, we give an example of the influence of simulation artefacts on network behaviour and spike-timing-dependent plasticity (STDP), underlining the importance of spike-time accuracy for the simulation of STDP.

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Section: Review Of Timing Errorsmentioning

confidence: 99%