Chuan Li, Vasilios Alexiades
Abstract:
Electrical propagation in excitable tissue, such as nerve
fibers and heart muscle, is described by a parabolic PDE
for the transmembrane voltage
,
known as the cable equation,
where
and
are the axial resistance and membrane
capacitance. The source term
represents the total ionic
current across the membrane, governed by the Hodgkin-Huxley or other
more complicated ionic models.
is an applied stimulus
current.
We compare the performance of various low and high order
time-stepping numerical schemes, including DuFort-Frankel
and adaptive Runge-Kutta, on the 1D cable equation.
Published September 25, 2010.
Math Subject Classifications: 65M08, 35K57, 92C37.
Key Words: Explicit schemes; super time stepping; adaptive Runge Kutta;
Dufort Frankel; action potential; Luo-Rudy ionic models.
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Chuan Li Mathematics Department, University of Tennessee Knoxville TN 37996, USA email: li@math.utk.edu | |
Vasilios Alexiades Mathematics Department, University of Tennessee Knoxville TN 37996, USA email: alexiades@utk.edu |
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