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High-order accurate difference schemes for the Hodgkin-Huxley equations
Department of Aeronautics and Astronautics, Stanford University, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2013 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, 573-590 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 252, 573-590 p.
Keyword [en]
High-order accuracy; Hodgkin–Huxley; Neuronal networks; Stability; Summation-by-parts; Well-posedness
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-96367DOI: 10.1016/ 000322633500029OAI: diva2:641022
Available from: 2013-08-15 Created: 2013-08-15 Last updated: 2016-10-10Bibliographically approved

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