On a variable step size modification of Hines' method in computational neuroscience
This work addresses the need for efficient and adaptive numerical integration in computational neuroscience, providing a practical improvement for simulating large-scale neural networks.
The paper introduces a one-step modification of Hines' method for simulating large neural networks that enables variable step size control, and demonstrates its stability and accuracy on Hodgkin-Huxley models, showing competitive performance compared to standard solvers.
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.