Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Consistent Initial Condition Calculation for Differential-Algebraic Systems
SIAM Journal on Scientific Computing
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Methods in Neuronal Modeling: From Ions to Networks
Methods in Neuronal Modeling: From Ions to Networks
The Designer's Guide to Spice and Spectre
The Designer's Guide to Spice and Spectre
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Exact simulation of integrate-and-fire models with synaptic conductances
Neural Computation
The NEURON Book
How much can we trust neural simulation strategies?
Neurocomputing
The high-conductance state of cortical networks
Neural Computation
Phenomenological models of synaptic plasticity based on spike timing
Biological Cybernetics - Special Issue: Object Localization
The quantitative single-neuron modeling competition
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
Firing patterns in the adaptive exponential integrate-and-fire model
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
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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.