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Numerical Methods and Analysis of Multiscale Problems pp 39–47Cite as

An Application in Neuroscience: Heterogeneous Cable Equation

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Abstract

We consider here a simplified version of an equation that models the voltage transmission along neurons, modeled here by a “cable.” If the thickness of the cable is much smaller than its length, it originates a singular perturbed behavior equation that does not differ substantially from what was investigated in Chap. 2 Moreover, other interesting asymptotics arise when considering a large number of synapses.

We also show here that the Multiscale Finite Element Method yields good approximations under all asymptotic regimes, even when the Galerkin Method fails.

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Authors and Affiliations

  1. Laboratório Nacional de Computação Científica-LNCC, Petrópolis, Brazil

    Alexandre L. Madureira

  2. Fundação Getúlio Vargas-FGV, Rio de Janeiro, Brazil

    Alexandre L. Madureira

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Madureira, A.L. (2017). An Application in Neuroscience: Heterogeneous Cable Equation. In: Numerical Methods and Analysis of Multiscale Problems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-50866-5_3

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