Fast and Accurate Explicit Integration Scheme for Biologically Detailed Neuron Simulations

Efficiency of numerical integration methods for a biologically detailed neuron model is examined. Because of the wide range of time constants, neuron equations are considered stiff. Stiffness is a property of a system in which the time step required to maintain stability for an explicit method is much smaller than the time step required to achieve a desired level of accuracy. Traditional explicit numerical methods optimised for non-stiff problems can be quite slow for the task.On the other hand, using implicit integration schemes designed to deal with extreme stiffness can be inefficient too. We investigate performance of an explicit Runge-Kutta Chebyshev (RKC) integration scheme, which is stabilized adaptively through a series of additional stages, for solving neuron equations. The method is compared to the Trapezoidal method (TR), a method currently implemented in several public domain neuron simulators. A comparison of the two numerical integration methods addresses: scalability with respect to CPU time and accuracy.