Plotting example for Nonlinear problems

[SebastianM-C]

I tried to simulate a 1D wave on a string with fixed ends and plotted the resulting animation and I'm posing the code here so that it could be refined into a tutorial.
The code is:

using ModelingToolkit
using MethodOfLines
using DomainSets
using NonlinearSolve
using Plots
# using SciMLNLSolve

@parameters t x
@variables E(..) u(..)

∂t = Differential(t)
∂tt = ∂t^2
∂xx = Differential(x)^2

c = 1

wave_eq1D = ∂tt(u(x, t)) ~ c^2 * ∂xx(u(x, t))

f(x) = sin(x)
g(x) = 0

bcs = [
    u(0, t) ~ 0,
    u(3, t) ~ 0,
    u(x, 0) ~ f(x),
    ∂t(u(x, 0)) ~ g(x)
]

t_min = 0.0
t_max = 2.0
x_min = 0.0
x_max = 3.0

# Space and time domains
domains = [
    t ∈ Interval(t_min, t_max),
    x ∈ Interval(x_min, x_max)
]

@named pde_system = PDESystem(wave_eq1D, bcs, domains, [t, x], [u(x, t)])

# Method of lines discretization
dx = 0.03
dt = 0.04

Nx = floor(Int64, (x_max - x_min) / dx) + 1

order = 2
discretization = MOLFiniteDifference([x => dx, t => dt], approx_order=2)

# Convert the PDE problem into an nonlinear problem
prob = discretize(pde_system, discretization)

sol = solve(prob, NewtonRaphson(), tol=1e-5)

anim = @animate for i in eachindex(t_min:dt:t_max)
    scatter(x_min:dx:x_max, sol[(i-1)*Nx+1:i*Nx], y_lims=(-1,1))
end

gif(anim, "wave.gif", fps=15)

The code needs a bit of cleanup and I'll also have to check if the chosen dt and dx make sense given the stability criteria. Moreover, the problem is a bit big for an example / tutorial since the string length is quite big with respect to the natural wavelength of the problem. I'll try to find more appropriate parameters over the following days.

Thanks to @xtalax for helping me with getting the above to work.