# FiniteVolumeMethod1D

Documentation for FiniteVolumeMethod1D.

This is a package for solving equations of the form

\[\dfrac{\partial u(x, t)}{\partial x} = \dfrac{\partial}{\partial x}\left(D\left(u, x, t\right)\dfrac{\partial u(x, t)}{\partial x}\right) + R(u, x, t),\]

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 Robin at $x=b$):

\[\begin{align*} \begin{array}{rrcl} \text{Neumann}: & \dfrac{\partial u(a, t)}{\partial t} & = & a_0\left(u(a, t), t\right), \\[9pt] \text{Dirichlet}: & u(a, t) & = & a_0\left(u(a, t), t\right), \end{array} \end{align*}\]

where the Dirichlet condition has $u(a, t)$ mapping from $a_0(u(a, t), t)$ (i.e., it is not an implicit equation for $u(a, t)$).

More information is given in the sidebar, and the docstrings are below.

If you want a more complete two-dimensional version, please see my other package FiniteVolumeMethod.jl.

`Modules = [FiniteVolumeMethod1D]`