Spectral method and high-order finite differences for nonlinear cable (Omurtag and Lytton 2010)

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We use high-order approximation schemes for the space derivatives in the nonlinear cable equation and investigate the behavior of numerical solution errors by using exact solutions, where available, and grid convergence. The space derivatives are numerically approximated by means of differentiation matrices. A flexible form for the injected current is used that can be adjusted smoothly from a very broad to a narrow peak, which leads, for the passive cable, to a simple, exact solution. We provide comparisons with exact solutions in an unbranched passive cable, the convergence of solutions with progressive refinement of the grid in an active cable, and the simulation of spike initiation in a biophysically realistic single-neuron model.
1 . Omurtag A, Lytton WW (2010) Spectral method and high-order finite differences for the nonlinear cable equation. Neural Comput 22:2113-36 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Neocortex V1 pyramidal corticothalamic L6 cell; Hodgkin-Huxley neuron;
Channel(s): I K,leak; I_K,Na;
Gap Junctions:
Simulation Environment: MATLAB;
Model Concept(s): Action Potential Initiation; Dendritic Action Potentials; Active Dendrites; Action Potentials; Methods;
Implementer(s): Omurtag, Ahmet [aomurtag at gmail.com];
Search NeuronDB for information about:  Neocortex V1 pyramidal corticothalamic L6 cell; I K,leak; I_K,Na;
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Omurtag A, Lytton WW (2010) Spectral method and high-order finite differences for the nonlinear cable equation. Neural Comput 22:2113-36[PubMed]

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