Equations

One of the goals of Impero is to provide a language for specifying partial differential equations as well as their discretization. For example, one can specify Burgers' equation fairly easily in Impero:

using Impero, Plots, GraphRecipes
@wrapper σ=nothing u=nothing
∂x = Operator(nothing, DerivativeMetaData(nothing, "x"))
∂t = Operator(nothing, DerivativeMetaData(nothing, "t"))
@pde_system pde_system = [
    σ = ∂x(u),
    ∂t(u) = -∂x(u * u - ∂x(σ)),
];

2-element Array{Equation,1}:
 σ=∂x()
 ∂t()=-(∂x())

We see that we have defined

println(pde_system[1])
println(pde_system[2])

σ=∂x(u)
∂t(u)=-(∂x(((u*u)+-(∂x(σ)))))

The code snippet does not perform any computation, but rather servers as a descriptor for the problem at hand. One can also plot the PDE system

p1 = plot(pde_system[1]); p2 = plot(pde_system[2]);
plot(p1)

and

plot(p2, size = (1000,1000))