Electrodiffusion Model Simulation of Rectangular Current Pulses in a Voltage-Biased Biological Channel

Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection–diffusion equation coupled either to Gaussʹ law or Poissonʹs equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection–diffusion equation. The rectangular wave shape of previously simulated traveling wave current pulses is preserved by the full set of partial differential equations for electrodiffusion.