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Toth TI, Crunelli V (1999) Solution of the nerve cable equation using Chebyshev approximations. J Neurosci Methods 87:119-36[PubMed]

References and models cited by this paper

References and models that cite this paper

Antal K, Emri Z, Toth TI, Crunelli V (1996) Model of a thalamocortical neurone with dendritic voltage-gated ion channels. Neuroreport 7:2655-8 [PubMed]

Carslaw HS, Jaeger JC (1959) Conduction of Heat in Solids (2nd ed)

De Schutter E, Bower JM (1994) An active membrane model of the cerebellar Purkinje cell. I. Simulation of current clamps in slice. J Neurophysiol 71:375-400 [Journal] [PubMed]

   Cerebellar purkinje cell (De Schutter and Bower 1994) [Model]

Destexhe A, Contreras D, Steriade M, Sejnowski TJ, Huguenard JR (1996) In vivo, in vitro, and computational analysis of dendritic calcium currents in thalamic reticular neurons. J Neurosci 16:169-85 [Journal] [PubMed]

   Thalamic reticular neurons: the role of Ca currents (Destexhe et al 1996) [Model]

Eaton JW (1995) Octave Manual www.che.wisc.edu-octave

Eccles JC (1957) The Physiology Of Nerve Cells

Funaro D (1992) Polynomial Approximation of Differential Equations

Funaro D (1992) Approximation by the Legendre collocation method of a model problem in electrophysiology J Comput Appl Math 43:261-271

Gottlieb D, Orszag SA (1977) Numerical analysis of spectral methods: theory and applications Cbms-nsf Regional Conference Series In Applied Mathematics

Hairer E, Wanner G (1991) Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems Springer Series In Computational Mathematics

Hines M (1997) NEURON http:::www.neuron.yale.edu

Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Jack JJB, Noble D, Tsien RW (1983) Linear cable theory Electrical Current Flow in Excitable Cells, Jack JJB:Noble D:Tsien RW, ed. pp.25

Jaeger D, De Schutter E, Bower JM (1997) The role of synaptic and voltage-gated currents in the control of Purkinje cell spiking: a modeling study. J Neurosci 17:91-106 [PubMed]

   Cerebellar purkinje cell (De Schutter and Bower 1994) [Model]

Kelvin WT (1855) On the theory of the electric telegraph Proc R Soc 7:382-399

Kirchhoff FU (1847) U8 ber die Auflosung von Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Strome gefu hrt wird Ann Phys Chem 72:497-508

Larkum ME, Rioult MG, Luscher HR (1996) Propagation of action potentials in the dendrites of neurons from rat spinal cord slice cultures. J Neurophysiol 75:154-70 [Journal] [PubMed]

Mainen ZF, Joerges J, Huguenard JR, Sejnowski TJ (1995) A model of spike initiation in neocortical pyramidal neurons. Neuron 15:1427-39 [PubMed]

   Spike Initiation in Neocortical Pyramidal Neurons (Mainen et al 1995) [Model]

Major G, Larkman AU, Jonas P, Sakmann B, Jack JJ (1994) Detailed passive cable models of whole-cell recorded CA3 pyramidal neurons in rat hippocampal slices. J Neurosci 14:4613-38 [PubMed]

Mascagni MV (1989) Numerical methods for neuronal modeling. Methods in Neuronal Modeling, Kock C:Segev I, ed.

Munsch T, Budde T, Pape HC (1997) Voltage-activated intracellular calcium transients in thalamic relay cells and interneurons. Neuroreport 8:2411-8 [PubMed]

Ohm GS (1827) Galvanische Kette Mathematisch Bearbeitet

Poznanski RR (1988) Membrane voltage changes in passive dendritic trees: a tapering equivalent cylinder model. IMA J Math Appl Med Biol 5:113-45 [PubMed]

Poznanski RR (1996) Transient response in a tapering cable model with somatic shunt. Neuroreport 7:1700-4 [PubMed]

Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical Recipes The Art Of Scientic Computing, University CAMBRIDGEPRESS, ed.

Rall W (1977) Core conductor theory and cable properties of neurons Handbook of Physiology. The Nervous System. Cellular Biology of Neurons, Kandel ER, ed. pp.39

Rall W (1989) Cable theory for dendritic neurons Methods In Neuronal Modeling: From Synapses To Networks, Koch C:Segev I, ed. pp.9

Strain J (1995) Spectral methods for nonlinear parabolic systems J Comput Phys 122:1-12

Stuart G, Spruston N, Sakmann B, Hausser M (1997) Action potential initiation and backpropagation in neurons of the mammalian CNS. Trends Neurosci 20:125-31 [PubMed]

Toth TI, Williams SR, Crunelli V (1996) Two types of bistable behaviour in thalamocortical neurones Proceedings of Cybernetics and Systems 96 :530-535

Trefethen LN (1997) Pseudospectra of linear operators Siam Rev 39:383-406

Trefethen LN, Trummer MR (1987) An instability phenomenon in spectral methods Siam J Numer Anal 24:1008-1023

Zhou Q, Godwin DW, O'Malley DM, Adams PR (1997) Visualization of calcium influx through channels that shape the burst and tonic firing modes of thalamic relay cells. J Neurophysiol 77:2816-25 [Journal] [PubMed]

Hines ML, Carnevale NT (2003) Personal Communication of NEURON bibliography

Lindsay KA, Ogden JM, Rosenberg JR (2002) An investigation into the influence of boundary condition specification in finite difference methods on the behaviour of passive and active neuronal models. Prog Biophys Mol Biol 78:3-43 [PubMed]

Omurtag A, Lytton WW (2010) Spectral method and high-order finite differences for the nonlinear cable equation. Neural Comput 22:2113-36 [Journal] [PubMed]

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

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