Solving the Heat Equation, changing the boundary conditions

[roflmaostc]

Seems like I need to register my custom boundary function like:

However, the docs were slightly outdated so I created a PR to fix it

# ╔═╡ 1ac45f27-dc97-4a29-bb42-ceff7ab6cc90
using OrdinaryDiffEq, ModelingToolkit, MethodOfLines, DomainSets


# ╔═╡ 10dee07a-9f74-4fb5-bc2b-f700c98047f9
using Plots

# ╔═╡ c50abfc0-fb9f-11ef-31e1-3395be6ca662
begin
	# Method of Manufactured Solutions: exact solution
	
	
	# Parameters, variables, and derivatives
	@parameters t x
	@variables u(..)
	Dt = Differential(t)
	Dxx = Differential(x)^2
	
	initial(x) = x == 0
	@register_symbolic initial(x)
	
	
	# 1D PDE and boundary conditions
	eq  = Dt(u(t, x)) ~ Dxx(u(t, x))
	bcs = [u(0, x) ~ initial(x),
		   u(t, 1) ~ 0,
		   u(t, -1) ~ 0]
	
	# Space and time domains
	domains = [t ∈ Interval(0.0, 0.1),
	           x ∈ Interval(-1, 1.0)]
	
	# PDE system
	@named pdesys = PDESystem(eq, bcs, domains, [t, x], [u(t, x)])
	
	# Method of lines discretization
	dx = 0.1
	order = 2
	discretization = MOLFiniteDifference([x => dx], t)
	
	# Convert the PDE problem into an ODE problem
	prob = discretize(pdesys,discretization)
	
	# Solve ODE problem
	sol = solve(prob, Tsit5(), saveat=0.02)
	
	# Plot results and compare with exact solution
	discrete_x = sol[x]
	discrete_t = sol[t]
	solu = sol[u(t, x)]
	
	plt = plot()
	
	for i in eachindex(discrete_t)
	    plot!(discrete_x, solu[i, :], label="Numerical, t=$(discrete_t[i])")
	end
	plt
	
end