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High-order accurate difference schemes for the Hodgkin-Huxley equations
Department of Aeronautics and Astronautics, Stanford University, Stanford, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)Report (Other academic)
Abstract [en]

A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate dierence schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the rst 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 dierential 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
Linköping: Linköping University Electronic Press, 2012. , 23 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2012:9
Keyword [en]
High-order accuracy; Hodgkin-Huxley; Neuronal networks; Stability; Summation-by-parts; Well-posedness
National Category
URN: urn:nbn:se:liu:diva-80739ISRN: LiTH-MAT-R--2012/09--SEOAI: diva2:548107
Available from: 2012-08-31 Created: 2012-08-29 Last updated: 2014-01-21Bibliographically approved

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Nordström, Jan
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Computational MathematicsThe Institute of Technology

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