%0 Journal Article
%T Comparison of time stepping schemes on the cable equation
%A Chuan Li
%A Vasilios Alexiades
%J Electronic Journal of Differential Equations
%D 2010
%I Texas State University
%X Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a parabolic PDE for the transmembrane voltage $V(x,t)$, known as the cable equation, $$ frac{1}{r_a}frac{partial^2V}{partial x^2} = C_mfrac{partial V}{partial t} + I_{m ion}(V,t) + I_{m stim}(t) $$ where $r_a$ and $C_m$ are the axial resistance and membrane capacitance. The source term $I_{m ion}$ represents the total ionic current across the membrane, governed by the Hodgkin-Huxley or other more complicated ionic models. $I_{m stim}(t)$ is an applied stimulus current.
%K Explicit schemes
%K super time stepping
%K adaptive Runge Kutta
%K Dufort Frankel
%K action potential
%K Luo-Rudy ionic models
%U http://ejde.math.txstate.edu/conf-proc/19/l1/abstr.html