An Application in Neuroscience: Heterogeneous Cable Equation

  • Alexandre L. Madureira
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


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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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Alexandre L. Madureira
    • 1
    • 2
  1. 1.Laboratório Nacional de Computação Científica-LNCCPetrópolisBrazil
  2. 2.Fundação Getúlio Vargas-FGVRio de JaneiroBrazil

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