I made this repository to practice using Julia for solving and visualizing partial differential equations. Right now there is only code for solving the heat equation and wave equation in 1D with Dirichlet boundary conditions.

After getting your Julia environment set up, run

julia --project=. main.jl

to reproduce the plots.

Uniform 0 initial conditions, with both ends of the rod held at 1.

uₜ = uₓₓ

u(0, t) = u(10, t) = 1

u(x, 0) = 0

The initial condition is 1 everywhere, with the boundaries set to 0.

uₜ = uₓₓ

u(0, t) = u(10, t) = 0

u(x, 0) = 1

0 initial condition, with one boundary condition at zero and the other at 1.

uₜ = uₓₓ

u(0, t) = 0

u(10, t) = 1

u(x, 0) = 0

Standing sine wave.

uₜₜ = uₓₓ

u(0, t) = u(10, t) = 0

u(x, 0) = sin(π x / 5)

uₓ(x, 0) = 0

uₜₜ = 4 uₓₓ

u(0, t) = u(1, t) = 0

uₓ(x, 0) = -x

u(x, 0) = x