FiniteVolumeMethod1D

This is a package for solving equations of the form

$$ \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\left(D(u, x, t)\frac{\partial u}{\partial x}\right) + R(u, x, t) $$

using the finite volume method over intervals $a \leq x \leq b$ and $t_0 \leq t \leq t_1$, with support for the following types of boundary conditions (shown at $x = a$, but you can mix boundary condition types, e.g. Neumann at $x=a$ and Dirichlet at $x=b$):

• Neumann: $\dfrac{\partial u(a, t)}{\partial x} = a_0\left(u(a, t), t\right)$.
• Dirichlet: $u(a, t) = a_0\left(u(a, t), t\right)$ (this is not an implicit equation for $u(a, t)$, rather $u(a, t)$ is mapped from $a_0\left(u(a, t), a, t\right)$.

For examples on how to use it, please see the docs. If you want a more complete two-dimensional version, please see my other package FiniteVolumeMethod.jl.