On a variable step size modification of Hines' method in computational neuroscience

TL;DR

This paper introduces a variable step size modification of Hines' method for simulating large neural networks, enhancing efficiency and stability by enabling step size control and error estimation.

Contribution

A one-step, variable step size version of Hines' method is developed, analyzed for stability, and implemented, improving simulation efficiency for neural network models.

Findings

The new method allows step size control and error estimation.

It demonstrates improved stability over the original method.

Performance comparisons show advantages over standard solvers.

Abstract

For simulating large networks of neurons Hines proposed a method which uses extensively the structure of the arising systems of ordinary differential equations in order to obtain an efficient implementation. The original method requires constant step sizes and produces the solution on a staggered grid. In the present paper a one-step modification of this method is introduced and analyzed with respect to their stability properties. The new method allows for step size control. Local error estimators are constructed. The method has been implemented in matlab and tested using simple Hodgkin-Huxley type models. Comparisons with standard state-of-the-art solvers are provided.