Cable Equation Simulation

Heng Gao
Fudan University

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The cable equaition is one of the most crucial equations in theoretical neuroscience, which can be regarded as a simple case of nonlinear reaction-diffusion equations, proposed by R. A. Fisher (1890-1962).
In this code repository, we simulate the cable equation via forward difference scheme.

The Cable equation

The Cable equation takes the form as follows

$$v_t(x,t) + \frac{1}{\tau} v(x,t)-\frac{\lambda^2}{\tau} v_{xx}(x,t)=0, \quad (x, t) \in \Omega\times[0, T],$$ $$v = 0 , \quad(x, t)\in \partial \Omega \times [0, T],$$ $$v(x, 0) = \mu(x), \quad (x, t)\in \Omega\times { t=0 },$$

where $\tau, \lambda, T$ are constants, $\Omega=[0, l]$, $l$ is the length of the cable, $\mu(x)$ is bounded on $\Omega$, $\mu(x)\in C^1(\Omega)$, satisfying $\mu(0)=\mu(l)=0$.

Usage

Directly run the cablesim.m using Matlab on your own computer.