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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.
Omurtag A, Lytton WW (2010) Spectral method and high-order finite differences for the nonlinear cable equation.
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Neuron or other electrically excitable cell;
Neocortex V1 pyramidal corticothalamic L6 cell;
Action Potential Initiation;
Dendritic Action Potentials;
Omurtag, Ahmet [aomurtag at gmail.com];
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Neocortex V1 pyramidal corticothalamic L6 cell
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