High-order accurate difference schemes for the Hodgkin-Huxley equations
Abstract
A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.
Keywords
Cite
@article{arxiv.1209.5687,
title = {High-order accurate difference schemes for the Hodgkin-Huxley equations},
author = {David Amsallem and Jan Nordstrom},
journal= {arXiv preprint arXiv:1209.5687},
year = {2015}
}